Preheat the oven to 325°F (163°C).
In a mixing bowl, cream together softened butter and sugar until light and fluffy.
Add the egg and vanilla extract, mixing until fully incorporated.
In a separate bowl, whisk together flour, baking powder, and salt.
Gradually add the dry mixture to the wet ingredients, mixing until a dough forms.
Press the dough evenly into the bottom of a 9-inch springform pan.
Bake the crust for 10-12 minutes, or until lightly golden.
While the crust cools, prepare the cheesecake filling.
In a large bowl, beat softened cream cheese until smooth.
Add granulated sugar and beat until well combined.
Beat in the eggs, one at a time, ensuring each is fully incorporated.
Mix in the vanilla extract and flour until smooth.
Pour the cheesecake filling over the cooled crust.
Bake for 40-45 minutes, or until the edges are set and the center is slightly jiggly.
Turn off the oven, crack the door, and let the cheesecake cool in the oven for 1 hour.
Remove from the oven and let it cool to room temperature before refrigerating.
Chill the cheesecake for at least 4 hours or overnight for best results.
Slice and serve, garnishing with sprinkles or whipped cream if desired.
