How to Make It
Heat oven to 275°F. Line a standard rimmed baking sheet with parchment paper. Set aside.
Beat egg whites in the bowl of a stand mixer fitted with the whisk attachment over medium-high until very frothy, 3 to 4 minutes. Add cream of tartar, beat 2 minutes. (You can also do this with a hand mixer, but your arm might get tired)
Combine sugar, cornstarch, and baking powder in a medium bowl. Lower mixer speed to medium; add sugar mixture 1 tablespoon at a time until stiff peaks form, 6 to 8 minutes. Add vanilla and whip until mixture returns to stiff peaks, 2 minutes more.
Using a rubber spatula or the back of a large spoon, spread meringue onto parchment-lined sheet, leaving a 1 inch border. Transfer to the oven and reduce temperature to 225°F. Bake until meringue is crisp and dry and an exterior shell has formed, 2½-3 hours. Turn oven off and let meringue cool completely in the oven overnight.
Meanwhile, make the curd: Combine blood orange and grapefruit juices in a medium saucepan over medium-high heat. Bring to a boil then reduce heat and simmer until reduced slightly, 3 to 4 minutes. Transfer to a liquid measuring cup (you should have about 1½ cups). Allow to cool to room temperature; stir in ginger and citrus zest.
In a separate bowl, whisk together eggs, yolks, and sugar. Whisk juice into egg mixture, return to saucepan, and cook over medium-low until mixture has thickened to pudding-like consistency, stirring often, 14 to 16 minutes. Pour through a fine-mesh sieve into a bowl, pressing the mixture through with a rubber spatula. Add the butter and salt to the bowl while curd is warm and stir until smooth. Cover with plastic wrap, pressing the wrap directly onto the curd, and refrigerate at least 2 hours (or up to 2 days).
When ready to serve, beat heavy cream, powdered sugar, and vanilla with an electric mixer on medium-high speed until soft peaks form, 1½ to 2 minutes. Spread onto meringue, leaving a 1-inch border. Dollop curd on top of whipped cream and swirl with a knife or skewer. Cut away peel and pith from blood orange and grapefruit. Slice the orange and supreme the grapefruit. Arrange fruit over cream and curd and top with mint.