Melt butter in a 9”–10” cast-iron (or other ovenproof) skillet. Scoop out 2 tablespoons melted butter and reserve. Add the apples to the pan and sauté until they begin to soften and brown. Add brown sugar and stir until sugar melts. Remove from heat and set aside.
Mix flour and salt in a medium bowl. In a separate bowl, beat the eggs with milk, vanilla and reserved melted butter. Whisk into flour mixture, stirring just until combined (some lumps will remain).
Pour batter over the apples and place in oven. Bake 15–18 minutes, until puffed and golden. Sprinkle with powdered sugar, if desired. Cut into wedges and serve.