For the crust: Preheat the oven to 350 degrees F. Spray a 13-by-9-inch glass baking dish with cooking spray.
Combine the cake mix, vanilla and egg whites in the bowl of an electric mixer fitted with the paddle attachment. Beat on medium speed until smooth, about 1 minute. Add the butter and mix just until combined. Spread the mixture evenly in the prepared baking dish.
For the filling: Beat the cream cheese in a clean mixer bowl with the paddle on medium speed until light and smooth, scraping the sides occasionally, 1 to 2 minutes. Add the vanilla and egg whites and beat until smooth. Add the butter and beat until smooth. Add the confectioners' sugar and beat on low speed to incorporate, and then beat on medium until light and smooth, about 1 minute. Stir in the sprinkles. Pour over the cake layer and smooth the top with a spatula.
Bake until the edges are puffed and golden brown and the center is just set, 35 to 40 minutes. Let cool on a rack. Dust with confectioners' sugar and a scattering of sprinkles. To serve, cut into squares and top each serving with a scoop of ice cream.
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