Step 1

Place 1 1/2 sticks unsalted butter in the bowl of a stand mixer (or large bowl if using an electric hand mixer). Let sit at room temperature until softened. Meanwhile, make the caramel.

Step 2

Place 1 cup granulated sugar and 1/2 cup water in a small, deep saucepan over medium-high heat and cook without stirring until the mixture changes to a medium to dark amber color (swirl the pan occasionally if it is not cooking evenly), 9 to 10 minutes. About 5 minutes into cooking, place 1/2 cup heavy cream in a microwave-safe measuring cup or small bowl and microwave on high until warm, about 30 seconds. Cover to keep warm.

Step 3

When the sugar mixture is ready, remove the pan from the heat. Add the warm cream (be very careful, as the cream will likely cause the caramel to bubble up dramatically) and stir with a wooden spoon until combined. If the cream has caused the caramel to harden, return the pan to medium heat and cook until melted again, then remove the pan from the heat.

Step 4

Add 1/4 cup white miso paste, 1 tablespoon unsalted butter, and 1 teaspoon vanilla extract, and stir and smash against the bottom of the pan until incorporated. Transfer the mixture into a fine-mesh strainer and press through the strainer into a small bowl. Let cool to room temperature, about 30 minutes, or speed it up by refrigerating and stirring periodically.

Step 5

Arrange 2 racks to divide the oven into thirds and heat the oven to 350ºF. Line 2 baking sheets with parchment paper.

Step 6

Add 1/2 cup packed light brown sugar, 1 teaspoon of the ground cardamom, 3/4 teaspoon kosher salt, and 1/2 teaspoon vanilla extract to the bowl of butter. Beat with the paddle attachment on medium-high speed until lightened in color and fluffy, scraping down the bowl as needed with a flexible spatula, about 2 minutes.

Step 7

Add 1 large egg and beat on medium speed until combined. With the mixer on the lowest speed, add 2 cups all-purpose flour and beat until just a few streaks of flour remain. Finish mixing by hand with a flexible spatula until the flour is just incorporated.

Step 8

Place 1/3 cup granulated sugar, 1/2 teaspoon ground cinnamon, and the remaining 1 teaspoon ground cardamom in a wide, shallow bowl and stir with a fork to combine. Scoop the dough out by level tablespoons and roll each into a ball. Roll each ball in the cardamom sugar and place on the baking sheets, spacing them evenly apart. Make an indentation about 1/2-inch deep with your thumb into each ball.

Step 9

Bake for 7 minutes. Rotate the baking sheets between racks and from front to back. Bake until the cookies take on a tiny bit of color (they don’t really brown) and are dry to the touch, 5 to 7 minutes more. If the indentations have lost their shape, remake them with the handle end of a wooden spoon. Let the cookies cool completely on the baking sheets.

Step 10

Fill each cookie indentation with the cooled caramel. Let sit until the caramel sets slightly, about 20 minutes, before serving.