Baked Alaska Flambé

Name: Baked Alaska Flambé
Ingredients: Nonstick cooking spray or butter, for greasing; 1 1⁄2 cups (13 oz.) nutty ice cream, such as pistachio; 11 oz. finely chopped bittersweet chocolate, divided; 3 cups (24 oz.) fruity ice cream (not sorbet), such as strawberry; 2 cups (20 oz.) vanilla ice cream; 1 stick (4 oz.) unsalted butter, plus more for greasing; 6 large egg yolks (plus half of a reserved egg shell, gently washed and dried; 3⁄4 cup plus 1 Tbsp. (3 oz.) pistachio or almond flour; 1⁄2 cup (3 oz.) rice flour; 6 large egg whites; 3⁄4 cup plus 2 Tbsp. (7 oz.) superfine sugar