Pineapple Upside-Down Cake

1. Adjust oven rack to lower-middle position and heat oven to 350 degrees. Grease 9-inch round cake pan, line with parchment paper, grease parchment, and flour pan.
2. FOR THE TOPPING: Cook pineapple and brown sugar in 10-inch skillet over medium heat until pineapple is translucent and has light brown hue, 15 to 18 minutes, stirring occasionally during first 5 minutes. Transfer fruit and juices to fine-mesh strainer set over bowl (you should have about 2 cups cooked fruit). Return juices to skillet and simmer over medium heat until thickened, beginning to darken, and mixture forms large bubbles, 6 to 8 minutes, adding any more juices released by fruit to skillet after about 4 minutes. Off heat, whisk in butter and vanilla. Pour caramel mixture into prepared cake pan and set aside while preparing cake. (Pineapple will continue to release liquid as it sits; do not add this liquid to already-reduced juice mixture.)
3. FOR THE CAKE: Whisk flour, baking powder, and salt in medium bowl. Using stand mixer fitted with paddle, beat butter and sugar on medium-high speed until pale and fluffy, about 3 minutes. Reduce speed to medium, add vanilla, and beat to combine. Increase speed to medium-high, add eggs and egg white, 1 at a time, and beat until combined. Reduce speed to low and add flour mixture in 3 additions, alternating with 2 additions of milk, scraping down bowl as needed (batter will be thick). Give batter final stir by hand.
4. Working quickly, distribute drained pineapple in cake pan in even layer, gently pressing fruit into caramel. Using rubber spatula, drop mounds of batter over fruit, then spread batter over fruit and to sides of pan in even layer. Gently tap pan on counter to release air bubbles. Bake cake until golden brown and toothpick inserted in center comes out clean, 45 to 50 minutes. Cool 10 minutes on wire rack, then place inverted serving platter over cake pan. Invert cake pan and platter together, then remove pan. Let cool to room temperature, about 2 hours, and serve.

ORANGE-CARDAMOM PINEAPPLE UPSIDE-DOWN CAKE
Add 1 tablespoon grated orange zest to skillet with pineapple in step 2, and add 1⁄4 cup orange juice to skillet in step 2 after draining pineapple and returning juices to skillet. Whisk 3⁄4 teaspoon ground cardamom into flour mixture in step 3.

COCONUT-GINGER PINEAPPLE UPSIDE-DOWN CAKE
Add 2 teaspoons grated fresh ginger to skillet with pineapple in step 2. Beat 3⁄4 cup sweetened shredded coconut with butter and sugar in step 4. Substitute 1⁄2 cup room-temperature coconut milk for whole milk.