Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.

In a large bowl, cream together the butter and granulated sugar until fluffy. Add the egg and vanilla extract, and mix until smooth.

In another bowl, whisk together the flour, baking powder, and salt. Gradually add this mixture to the wet ingredients and mix until a dough forms.

In a separate bowl, beat the cream cheese until smooth. Add the powdered sugar and vanilla extract, mixing until the filling is smooth and lump-free.

Using a cookie scoop or spoon, form balls of dough (about 1 tablespoon each) and place them on the prepared baking sheet. Use your thumb or a spoon to make an indentation in the center of each cookie ball.

Spoon a small amount of cheesecake filling into the indentation of each cookie dough ball.

Bake the cookies for 12-15 minutes, or until the edges are golden brown. Remove from the oven and let them cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.