Preheat oven to 350°.
Beat butter with a mixer at medium speed until light and fluffy. Add sugar, vanilla, and egg; beat until smooth.
Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, cocoa, baking powder, and salt. Add flour mixture, alternately with egg mixture and milk. (Batter will be very stiff.)
Transfer mixture to a 9-inch pie plate coated with cooking spray, spreading evenly on bottom.
Bake at 350° for 15 to 17 minutes or until a wooden pick inserted in center comes out clean. Cool completely on a wire rack.
Spoon yogurt into brownie crust, smoothing the top. Cover and freeze until firm.
Spread whipped topping over top of pie. Cover and freeze until firm.
Cut pie into 10 slices. Drizzle each slice of pie with 1 tablespoon chocolate syrup, and top with a cherry.