In a large bowl, whisk together the flour, cocoa, baking powder, baking soda, and salt; set aside. In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and both sugars on medium speed until light and fluffy, 2 to 3 minutes. Add the egg and vanilla; beat to combine. With the mixer on low speed, add flour mixture, and beat to combine, scraping down the sides of the bowl as needed.
Press dough into 10-inch springform pan as instructed in Raspberry-Swirl Cheesecake recipe.