To make the cheesecake filling: Combine the cream cheese, sugar, and vanilla in a bowl. Use a whisk or hand mixer and mix until smooth.
Using a piping bag, dollop the filling by the tablespoonful onto a parchment lined baking sheet. Freeze for at least 1 hour.
Meanwhile, to make the cookies, combine the flour, baking soda, salt, cinnamon, and nutmeg in a bowl.
In a stand mixer, combine the butter, brown sugar, and sugar. Mix until light and fluffy, 2-3 minutes.
Mix in the carrots, vanilla, and egg yolks.
Add the dry ingredients, and stir to combine.
Preheat oven to 350 degrees. Line 2 sheet pans with parchment paper.
Using a 2 ounce cookie scoop, scoop the cookies, and make an indent in the cookie dough while still in the scoop.
Place a cheesecake dollop in the center, and press together the dough to make a ball. Place on parchment lined sheet pan.
Freeze the cookies for 10-15 minutes.
Bake 13-15 minutes, or until golden brown on the edges. Allow to sit and cool on the pan for 10-15 minutes before moving to a wire rack to cool completely.
To make the carrot decorations, combing the cream cheese, butter, powdered sugar, and vanilla until smooth and creamy. Divide into 2 separate bowls: 3/4 of the frosting dyed orange, and 1/4 of the frosting dyed green. Make carrots on the tops of the cookies.
Keep refrigerated for 4-5 days, or freeze for up to 3 months.
