**Preheat the Oven:** Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone baking mat.

**Make the Cheesecake Filling:** In a medium mixing bowl, beat the cream cheese, granulated sugar, vanilla extract, and egg yolk until smooth and creamy. Set aside.

**Make the Carrot Cake Cookie Dough:** In a separate bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt. In a large mixing bowl, beat the softened butter, granulated sugar, and brown sugar until light and fluffy. Add the egg and vanilla extract, mixing until combined. Gradually add the dry ingredients to the wet mixture, stirring until just combined. Fold in the grated carrots and walnuts (if using).

**Scoop the Cookies:** Using a spoon or cookie scoop, drop about 1 tablespoon of carrot cake dough onto the prepared baking sheet.

**Add the Cheesecake Filling:** Using a spoon, make a small indentation in the center of each cookie dough ball. Place about 1 teaspoon of cheesecake filling into the indentation.

**Top with More Dough:** Place a small amount of carrot cake dough on top of the cheesecake filling to cover it, forming a sandwich.

**Bake:** Bake for 10-12 minutes, or until the edges of the cookies are golden and the centers are set. Let the cookies cool on the baking sheet for 5 minutes, then transfer to a cooling rack to cool completely.

**Serve:** Enjoy these decadent cookies immediately or store for later!