1/2 cup packed light-brown sugar
1 medium ripe pineapple, peeled, cored and cut crosswise into 1/4-inch-thick slices
3 medium ripe mangos, peeled
1 stick unsalted butter (8 tablespoons)
In a medium bowl, sift together the flour, salt, baking soda, and baking powder; set aside. Place pineapple and mango slices in alternating slices around the pan, covering the bottom as much as you can.
In the bowl of an electric mixer fitted with the paddle attachment, beat the remaining butter with granulated sugar on medium speed until light and fluffy, 2 to 3 minutes. Add eggs, one at a time, beating well after each addition; scrape down the sides of the bowl as needed. Beat in the vanilla. With the mixer on lowest speed, add flour mixture in two parts, alternating with sour cream and beginning and ending with flour.