In a bowl, beat the cream cheese, powdered sugar, and vanilla extract until smooth. Cover and freeze for 30 minutes to firm up.
In a separate bowl, cream the butter and sugar until light and fluffy. Mix in the egg and vanilla. Gradually add the flour, baking powder, and salt, stirring until combined. Chill the dough for 15 minutes.
Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper. Scoop out a tablespoon of cookie dough and flatten it slightly. Place a small portion of the cheesecake filling in the center, then cover with another small piece of dough, sealing the edges.
Place the cookies on the baking sheet, spacing them apart. Bake for 10-12 minutes, or until the edges are lightly golden. Let them cool for 5 minutes on the sheet before transferring to a wire rack.