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Step 1
Preheat the oven to 350F (180C). Butter and flour an 8" bundt pan by greasing the pan with butter first, and then coating it with a very thin layer of flour.
Step 2
Combine the dry ingredients together. Add the flour, baking powder, cinnamon, nutmeg, ginger, allspice, cloves, and salt to a medium bowl. Whisk them together and set aside.+
Step 3
Combine the wet ingredients together. Add the yogurt, sugar, oil, eggs, and vanilla to a separate medium bowl and mix until combined and smooth.
Step 4
Pour the wet ingredients into the dry ingredients and mix until just combined and smooth. Pour the cake batter into your prepared bundt pan.
Step 5
Bake for 35-40 minutes or until golden on top and a toothpick inserted in the center of the cake turns out dry. Remove from the oven and allow to cool down in the pan before inverting it onto a plate. While the cake cools down completely, make the frosting.
Step 6
Frost. Melt the butter in a small pan over medium low heat. I recommend using a light-colored pan so you can easily see the color of the butter change but any will work. Once the butter has melted completely, allow it to sizzle and foam until it turns into a deep amber color. Turn off the heat, pour the butter through a sieve and into a medium bowl. Chill the brown butter until solid again, then beat it with a hand-mixer until fluffy and creamy. Add the cream cheese and beat until combined and smooth. Finally, add the powdered sugar, vanilla extract, and salt, and beat until smooth again. Add in the milk 1 tbsp per addition, mixing it in fully before adding more. You want to control how thick your frosting is so how much milk you use depends on how thick or pourable you want it to be. Pour the frosting over the top of your cooled cake and enjoy!