Prepare the Cream Cheese Filling – Beat the cream cheese until smooth, then mix in the sugar and vanilla extract. Scoop small dollops onto a lined baking sheet and freeze until solid.

Mix the Dry Ingredients – Sift together the flour, baking soda, salt, cinnamon, and nutmeg in a medium bowl.

Combine the Wet Ingredients – In a mixing bowl, beat the melted butter, brown sugar, and granulated sugar until combined. Add the grated carrots, vanilla extract, and egg yolks, then mix well.

Form the Dough – Gradually add the dry ingredients to the wet ingredients, mixing until fully combined. Let the dough rest for 10 minutes.

Assemble the Cookies – Scoop out cookie dough balls, pressing a small indent into the center. Place a frozen dollop of cream cheese filling inside and cover it completely with dough. Freeze the filled cookie dough balls for 10 minutes.

Bake to Perfection – Arrange cookies on a lined baking sheet and bake at 350°F for 13-15 minutes. Let them cool on the sheet for 10-15 minutes before transferring to a wire rack.

Optional Decoration – If decorating, beat the frosting ingredients together until smooth. Dye portions of the frosting orange and green, then pipe carrot shapes onto the cooled cookies.