1. Preheat oven to 350°. Melt butter in a lightly greased 10-inch cast-iron skillet or a 9-inch round cake pan (with sides that are at least 2 inches high) over low heat. Remove from heat. Sprinkle with brown sugar. Arrange 7 pineapple slices in a single layer over brown sugar, reserving remaining pineapple slices for another use. Place 1 cherry in center of each pineapple slice.
2. Beat granulated sugar, oil, and eggs at medium speed with an electric mixer until blended. Combine flour and next 4 ingredients; gradually add to sugar mixture, beating at low speed just until blended. Stir in carrots and pecans. Spoon batter over pineapple slices.
3. Bake at 350° for 45 to 50 minutes or until a wooden pick inserted in center comes out clean. Cool in skillet on a wire rack 10 minutes. Carefully run a knife around edge of cake to loosen. Invert cake onto a serving plate, spooning any topping in skillet over cake.