Using a hand mixer, beat the cream cheese on high until smooth. Blend in the sugar and vanilla extract until fully combined. Line a baking sheet with wax paper and, using a 1/2 tablespoon measure, portion out 14 dollops. Freeze until solid.

Finely grate carrots and press them between layers of paper towel to remove excess moisture. In a bowl, whisk together the flour, baking soda, salt, cinnamon, and nutmeg. In a separate bowl, beat the cooled melted butter with both sugars for two minutes on high speed. Incorporate the grated carrots, vanilla extract, and egg yolks, mixing on medium until integrated. Gradually add in the dry ingredients, mixing on low just until combined. Preheat the oven to 350°F and prepare two baking sheets with parchment paper. Let the dough rest for 10 minutes.

Scoop out dough using a large 2-ounce (or 2-tablespoon) cookie scoop. Press a deep indent into each dough ball with your thumb. Insert a frozen cheesecake center into each cavity and encase it fully with cookie dough. Freeze the formed cookies for 10 minutes. Arrange six dough balls per sheet and bake one sheet at a time for 13 to 15 minutes. Avoid moving them during baking to preserve the cream cheese center. Cool on the baking tray for 10–15 minutes before transferring to a wire rack. Store chilled for best flavor and texture.

If desired, beat the cream cheese and butter until fluffy. Mix in the powdered sugar and vanilla until smooth. Separate into two portions: color two-thirds orange and one-third green with gel dyes. Using piping tips (Wilton 4 and 65), pipe decorative carrots onto each cookie.