Place an oven rack in the lower 1/3 of the oven. Preheat the oven to 325 degrees F. Butter and flour a mini Bundt pan.
For the Cakes: Place the pineapple in the bowl of a food processor. Pulse until coarsely chopped. In a 10-inch nonstick skillet, combine the chopped pineapple, 2 tablespoons pineapple juice, sugar, and butter over medium-high heat. Bring the mixture to a boil, stirring occasionally. Cook until the liquid evaporates and the mixture begins to brown, about 10 to 15 minutes. Spoon the pineapple mixture into the prepared pan.
In a large mixing bowl, combine the egg whites, water, vegetable oil, almond extract, cake mix, and 2/3 cup pineapple juice. Using an electric hand mixer, beat the mixture on medium speed for 2 minutes. Pour the batter over the cooked pineapple. Bake for 28 to 30 minutes until the cakes begin to pull away from the sides of the pan and the tops are golden. Allow the cakes to cool for 15 minutes. Place a piece of parchment paper on top of the cakes. Put a baking sheet, upside-down, on top of the parchment paper. Flip both pans over and allow the cakes to cool completely while still in the Bundt pan, about 1 hour. Unmold the cakes and place on individual serving plates.
Cook's Note: This recipe will also work using 1 (20-ounce) can crushed pineapple in 100 percent pineapple juice, drained and juice reserved.