1. Preheat oven to 350°.
2. Coat a 9-inch springform pan or cake pan with 3-inch sides with cooking spray; line bottom of pan with parchment paper. Coat paper with cooking spray. If using a springform pan, wrap outside and bottom of pan tightly with a double layer of heavy-duty foil.
3. Drizzle melted butter over parchment in bottom of pan; sprinkle with brown sugar. Arrange cherries in a single layer over brown sugar. Place pan on a baking sheet lined with foil.
4. Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, salt, and baking soda, stirring with a whisk; set aside. Place granulated sugar, softened butter, and oil in a large bowl; beat with a mixer at medium speed until well blended (about 3 minutes). Beat in vanilla. Add eggs, 1 at a time, beating well after each addition. Add flour mixture and buttermilk alternately to oil mixture, beginning and ending with flour mixture (batter will be thick). Spread batter evenly over cherries in pan. Bake at 350° for 30 minutes.
5. Reduce oven temperature to 325° (do not remove cake from oven). Bake at 325° for 25 to 30 minutes or until a wooden pick inserted in center comes out clean. Cool in pan on a wire rack 10 minutes. Loosen cake from edges of pan with a knife; invert onto wire rack.