Martha and baker John Barricelli make a mouthwatering Pineapple Mango Upside-Down Cake.
Preheat oven to 350 degrees. Butter an 8-by-8-inch cake pan, line it with parchment paper, and butter parchment. Using a 3-inch cookie cutter, cut out rounds from centers of four of the pineapple slices. Using a 1 1/2-inch cookie cutter, cut out the centers of each of the four rounds, and discard; set rings aside. Finely chop enough of the remaining pineapple to yield 1 cup (reserve remainder for another use). Place chopped fruit in a fine sieve set over a bowl to drain.
Cut the mango lengthwise into 1/4-inch-thick slices. Using the 1 1/2-inch cookie cutter, cut out four rounds from mango slices; set aside. Finely chop enough of the remaining mango to yield 1/2 cup; add to the pineapple in the sieve.
In the bowl of an electric mixer fitted with the paddle attachment, beat 2 tablespoons butter with the brown sugar until light and fluffy, 2 to 3 minutes. Using a small offset spatula, evenly spread butter mixture in the bottom of the prepared pan; set aside.
In a medium bowl, sift together the flour, salt, baking soda, and baking powder; set aside. Place a reserved pineapple ring in each corner of the prepared pan. Place a reserved mango round in the center of each ring.
In the bowl of an electric mixer fitted with the paddle attachment, beat remaining stick of 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.
Transfer the chopped pineapple-mango mixture to cake pan; discard juice. Using a small offset spatula, carefully spread fruit in an even layer on top of cut-out fruit, making sure to fill all the empty spaces, including any gaps in the corners. Using the offset spatula, spread batter evenly over fruit.
Bake, rotating pan halfway through, until cake is golden brown and a cake tester inserted in the center comes out clean, about 50 minutes. Transfer pan to a wire rack to cool 30 minutes. Invert onto a cake plate; peel off the parchment paper. Serve cake slightly warm or at room temperature.