Preheat oven to 375 degrees. Butter 8-inch ovenproof skillet (preferably cast-iron); dust with flour, tapping out excess. Whisk together flour, baking powder, baking soda, and 1/2 teaspoon salt. Beat butter and 3/4 cup sugar with a mixer on medium speed until pale and fluffy. Beat in egg. Add flour mixture in 3 additions, alternating with buttermilk.
Pour batter into prepared skillet, and smooth top with an offset spatula. Fan plums on top, and sprinkle with remaining 2 tablespoons sugar. Bake until golden brown and a toothpick inserted into the center comes out clean, 35 to 40 minutes. Let cool slightly.