Preheat the oven to 350°F. Line an 8-inch square baking pan with parchment paper.

Brown 6 tablespoons of the butter until the milk solids turn golden and smell nutty. Pour into a bowl, add the remaining 4 tablespoons butter, stir until melted, and cool for about 10 minutes.

Whisk the sugar, egg, and vanilla into the butter. Fold in the flour, baking powder, and salt until a soft dough forms. Stir in sprinkles if using.

Press about two-thirds of the dough into the bottom of the pan. Chill the remaining dough while making the filling.

Beat the cream cheese and sugar until smooth. Mix in the sour cream, egg, vanilla, and cornstarch on low speed just until combined. Spread over the cookie base.

Crumble the reserved cookie dough over the cheesecake layer.

Bake for 34 to 40 minutes, until the cookie topping is lightly golden and the cheesecake center has only a slight wobble.

Cool completely, then refrigerate for at least 3 hours before slicing.