Beat cream cheese, sugar, and vanilla until creamy.
Line baking sheet with waxed paper.
Spoon dollops of mixture onto paper; freeze 30 mins.
Grate carrots finely; blot excess moisture.
Beat butter, brown sugar, granulated sugar until fluffy.
Add egg, vanilla, grated carrots; mix well.
Whisk flour, spices, baking soda; fold into butter mixture.
Preheat oven to 350°F; line baking sheets with parchment.
Scoop 2 tbsp dough, press frozen cream cheese ball inside.
Roll into balls; place on sheets, bake 12-14 mins.
Cool on sheet 3-5 mins; transfer to rack to cool completely.
Store cooled cookies in airtight container in fridge.