Preheat oven to 350°F (175°C). Grease a 9-inch springform pan.

Make the crust: In a medium bowl, whisk together flour, baking powder, and salt. In a large bowl, cream together butter and sugar until light and fluffy. Beat in egg and vanilla. Gradually add dry ingredients to wet ingredients, mixing until just combined. Press dough into the bottom of the prepared pan. Bake for 12-15 minutes, or until lightly golden. Let cool completely.

Preheat oven to 325°F (165°C).

Make the filling: In a large bowl, beat cream cheese and sugar until smooth. Beat in flour, salt, and vanilla. Add eggs one at a time, beating well after each addition. Stir in sour cream.

Pour filling over the cooled crust.

Place springform pan in a larger roasting pan. Pour hot water halfway up the sides of the springform pan (water bath).

Bake for 50-60 minutes, or until the cheesecake is set around the edges but the center is still slightly jiggly. Turn off oven; leave cheesecake in with the door slightly ajar for 1 hour. Cool completely, then refrigerate for at least 4 hours, or preferably overnight.