Combine brown sugar, pinch of salt, and 1/4 cup butter in a heavy saucepan; cook over medium heat, stirring occasionally, 5 to 7 minutes or until mixture bubbles and sugar melts.
Pour sugar mixture into a 10-inch cast-iron skillet.
Cut pineapple crosswise into 6 (1/4-inch-thick) rings. Arrange pineapple rings in a single layer over brown sugar mixture.
Beat remaining 1/4 cup butter and granulated sugar with an electric mixer at medium speed until creamy.
Add eggs, 1 at a time, beating until blended after each addition. Stir in vanilla.
Stir together flour, baking powder, and salt; add to butter mixture alternately with sour cream, beginning and ending with flour mixture. Beat batter at low speed until blended after each addition. Beat egg whites until stiff peaks form; fold into batter.
Pour batter over pineapple slices.
Bake at 325 for 40 to 45 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 onto a serving plate; spoon any topping in skillet over cake.
