In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large mixing bowl, beat the softened butter and granulated sugar together until light and fluffy, about 2-3 minutes.
Mix in the egg until fully incorporated.
Add the sourdough discard and vanilla extract, mixing until smooth.
Gradually add the dry ingredients and mix just until a soft dough forms. Avoid overmixing.
Transfer the dough to the prepared baking pan. Using lightly floured hands or an offset spatula, gently press the dough into an even layer, making sure it reaches all four corners.
Bake for 18-20 minutes, or until the edges are lightly golden and the center appears mostly set. The crust does not need to be completely browned since it will continue baking with the cheesecake.
Remove from the oven and set aside while preparing the filling.