Preheat oven to 325°F (163°C). Grease a 9-inch springform pan and line the bottom with parchment paper.
Make the sugar cookie dough: In a medium bowl, whisk flour, baking soda, baking powder, and salt. In a large bowl, cream butter, granulated sugar, and brown sugar until fluffy. Beat in eggs and vanilla. Add dry ingredients until combined.
Press half of the sugar cookie dough into the bottom of the prepared pan for the crust. Chill the rest for topping.
Make the cheesecake filling: In a large bowl, beat cream cheese and sugar until smooth. Add eggs one at a time, mixing after each. Mix in sour cream and vanilla until combined.
Pour filling over crust in springform pan. Drop spoonfuls of reserved cookie dough on top. Sprinkle with sprinkles.
Bake for 55–65 minutes, until edges are set but center is slightly jiggly. Turn off oven, crack door, and let cheesecake cool 1 hour.
Refrigerate cheesecake at least 6 hours or overnight before slicing and serving.
Notes
Chill cheesecake for at least 6 hours before serving. Store leftovers in the refrigerator for up to 5 days.