Preheat the oven to 325 degrees F (165 degrees C). Coat a 9-inch square baking pan with cooking spray.
Melt 1/2 cup butter in a saucepan over medium-high heat. Add 1 cup plus 2 tablespoons brown sugar, stirring until just dissolved. Cook until bubbling, about 2 minutes. Pour into the prepared pan.
Arrange pineapple in a single layer of diagonal rows over the brown sugar mixture.
Whisk together both flours, baking powder, cornstarch, and salt in a bowl.
Beat together white sugar and 1 cup butter in a large bowl with an electric mixer at medium speed until light and fluffy, 3 to 4 minutes. Beat in eggs, one at a time, then stir in vanilla. Beat in 1/2 of the flour mixture, followed by 1/2 of the sour cream; repeat.
Spread batter over pineapple in the pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 65 to 70 minutes.
Cool in the pan on a wire rack for 10 minutes, then invert onto a platter.