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Step 1
Brown the butter: Use a light-coloured pot to visualize the butter better. Over medium-high heat, melt 3/4 cup of unsalted butter. Once completely melted, stir the butter often with a heat-proof spatula to evenly cook the milk solids (the white specks). As the milk solids cook, they will start to brown, giving you nutty brown butter. This will take around 4-5 minutes total. Before the butter finishes browning, it will foam up. You can swirl the pan to check if the solids have browned. Once browned, remove from the pot and pour into a heat-proof bowl, scraping all the browned bits as well. If you are using a stand mixer, you can pour it directly into your kitchen aid bowl.
Step 2
Add in 2.5 Tbsp of sweet white miso paste to the hot brown butter. Mix the miso in with a spatula to slightly break up the miso. Ensure the miso is completely covered by the butter and then place it into the fridge to cool for 5-10 minutes until the mixture is just warm to touch.
Step 3
Remove miso butter from the fridge and in a stand mixer with a paddle attachment, or a bowl with a whisk, add 1/4 + 1/8 cup brown sugar and 1/2 cup granulated sugar. Cream butter and sugars for 1 minute, until well combined.
Step 4
Add in 1 egg and 1 tsp vanilla extract and mix for 1-2 min until slightly pale and thick.
Step 5
Add in 1/4 + 1/8 cup finely grated carrot, that has been squeezed dry, along with 2 tsp of ground cinnamon, 2 tsp of ground ginger, and 1/4 tsp freshly grated nutmeg. Mix for around 15 seconds or until well combined.
Step 6
If you are using a bowl, switch to a rubber spatula. Add in baking soda and all-purpose flour and mix until the flour is just mixed in. Do not over-mix! The cookie dough will be slightly wet and difficult to scoop, so set the dough into the fridge to firm up for 30 minutes, before scooping.
Step 7
Using a large cookie scoop (around 2-3 tbsp), scoop your cookies onto a tray lined with parchment paper or a silicone mat. To ensure your cookies are fairly uniform, when you scoop your dough, ensure that the bottom of the cookie has a flat edge and the top is rounded. Place the scooped cookies into the fridge again for at least 30 minutes, or freeze for 15 minutes till cookies are firm to touch. You do not need to cover your cookies with saran wrap! (You should get around 16 cookies, giving you 8 sandwiches. But you're welcome to make them as big or as small as you like)
Step 8
Preheat your oven to 350° Fahrenheit. Place cookies a few inches apart and bake for 10 minutes in the middle rack of the oven. After 10 minutes, the cookies will be puffed up but not fully cooked. Remove from the oven and tap the entire tray 3-4 times to deflate the cookies. Return the tray into the oven for another 3-4 minutes, or until cookies are slightly golden on the edges and the middle is still soft. You do not want to overbake these cookies! Remove from the oven and tap the tray again, 2-3 times until they deflate slightly. Let cookies cool completely.
Step 9
While your cookies are cooling, work on the miso caramel. In a small pot, with high sides, add 1/2 cup of granulated sugar. Place the pot over medium heat and let the sugar start to melt and caramelize. Do not mix, just occasionally swirl the pot to allow the sugar to melt. Once the sugar turns deep amber and is 95-100% melted (may have small specks of sugar left) remove it from the heat. At this point, you can whisk to dissolve the remaining sugar. This takes anywhere from 3-6 minutes, but make sure you watch this carefully as the sugar can go from caramelized to burnt quickly!
Step 10
Off heat, add in 2 Tbsp of unsalted butter and 1 Tbsp of white miso and mix immediately. The caramel will start to bubble up, so be careful when mixing! At first, it will look like the caramel has split, but continue to mix until well combined. The caramel will be thick and almost lumpy at this point.
Step 11
Turn back the heat to medium and slowly pour in 1/3 cup of warm heavy cream, while constantly whisking until the caramel is smooth. Heat the caramel on medium for around 3 minutes, whisking constantly until the caramel has thickened and reduced by almost half.
Step 12
Before removing from the heat, add in 1 tsp of vanilla extract and whisk in. Remove from heat and pour caramel into a heat-proof bowl. Caramel will still be runny at this point but will thicken as it cools.
Step 13
In a stand mixer with a whisk attachment or a bowl with a whisk, add in 1/2 cup softened cream cheese, 2 tbsp of softened unsalted butter, 1 tsp vanilla extract and a pinch of salt. Cream together till well combined.
Step 14
Add in half of the powdered sugar (around 3/4 cup), mixing well for around 1-2 minutes before adding the last half. At first, it will look thick, but do not add any cream or milk as this will soften quickly! After adding your last half, mix well for around 2-3 minutes, until slightly thickened, creamy and smooth.
Step 15
Transfer to a piping bag with a star tip. If your frosting is too runny, place it in the fridge to thicken for 30 minutes.
Step 16
With your cooled carrot cake cookie sandwiches, line them up, picking two cookies that are similar in size. Place the uniform cookies next to one another.
Step 17
Picking up one cookie from each sandwich, pipe the cream cheese frosting around the edges of the cookie, leaving a slight 1/2cm border around the outer edge. Leave the middle empty to fill with caramel. When you squish the top cookie together, it will push the cream out, which is why you need to leave a slight edge.
Step 18
Place around 1-2 tsp of miso caramel in the middle of the frosting. If your frosted cookie is too runny at this point, you can freeze the piped cookie halves for around 15-30 minutes to firm up.
Step 19
Place the matching cookie on top and give a slight squeeze. Serve immediately! For cookies not consumed the day of, please freeze in an airtight container for up to 3 weeks. Defrost for 30-60min, or until the cookie is soft and completely defrosted. Enjoy!