Make Cheesecake Filling: Beat together cream cheese, granulated sugar, and vanilla extract until smooth and creamy. Scoop into dollops on a tray and freeze for at least 30 minutes.

Prepare Carrot Cookie Dough: Grate fresh carrots finely and blot them with paper towels. Sift together flour, baking soda, salt, cinnamon, and nutmeg in a bowl.

Combine Wet Ingredients: In a large bowl, whisk melted butter with brown sugar and granulated sugar until fluffy. Add grated carrots, vanilla, and egg yolks, mixing until smooth.

Incorporate Dry Ingredients: Gradually add the dry mixture into the wet ingredients, folding gently until just combined to maintain tender texture.

Preheat Oven & Rest Dough: Preheat oven to 350°F. Let cookie dough rest for 15-20 minutes to fully hydrate the flour.

Form Cookies: Scoop dollops of dough onto baking sheets, create an indentation, place a frozen filling inside, and cover with more dough.

Bake Cookies: Bake for 13-15 minutes until golden around edges but still soft in center. Cool on sheets for 10-15 minutes before transferring to racks.

Optional Frosting: Beat together cream cheese and softened butter. Gradually add powdered sugar until smooth, then frost cooled cookies.