Preheat oven to 425°F.
Heat butter in an ovenproof 10-inch heavy skillet (preferably well-seasoned cast-iron) over moderate heat until foam subsides. Stir in brown sugar and remove from heat. Spread mixture evenly in skillet and arrange apples, overlapping, in 1 layer.
Blend flour, sugar, baking powder and soda, salt, and cinnamon in a food processor. Add butter and pulse until mixture resembles coarse meal. Transfer to a bowl and add buttermilk, stirring just until mixture is moistened.
Drop batter on top of apples and gently spread, leaving a 1-inch border around edge of skillet. (Cake needs room to expand.)
Bake cake in middle of oven until golden brown and firm to the touch, 25 to 30 minutes. Cool cake in skillet on a rack 3 minutes, then invert onto a platter. Replace any apples that stick to skillet on cake.