Preheat the oven to 350°F (175°C).
Prepare the crust by mixing flour, sugar, baking powder, and salt in a bowl.
In a separate bowl, cream together the softened butter and sugar until light and fluffy.
Add the egg and vanilla extract, mixing well until combined.
Gradually add the dry ingredients to the wet mixture, mixing just until combined.
Press the dough into the bottom of a greased springform pan.
In another bowl, beat the cream cheese until smooth and creamy.
Add sour cream, sugar, and vanilla extract, mixing until fully incorporated.
Add the eggs one at a time, mixing gently after each addition.
Pour the cheesecake filling over the prepared crust.
Bake in the preheated oven for 50-60 minutes, until the edges are set and the center is slightly jiggly.
Turn off the oven and leave the cheesecake inside for 1 hour to cool gradually.
Remove from the oven and allow to cool to room temperature before refrigerating for at least 4 hours.
Serve chilled, topped with optional whipped cream and sprinkles.