CAKE
Unsalted butter, for pans
2/3 cup all-purpose flour, plus more for pans
2/3 cup sugar, divided
1/2 cup unsweetened cocoa powder
1 teaspoon baking powder
1 teaspoon baking soda
1/2 teaspoon coarse salt
1/2 cup safflower oil
1/3 cup warm water
1 teaspoon pure vanilla extract
3 large eggs, room temperature, separated
MARSHMALLOW SWIRL
4 large egg whites, room temperature
1 cup sugar
1/4 teaspoon cream of tartar
1 teaspoon pure vanilla extract
ASSEMBLY
3 pints chocolate ice cream (6 cups), slightly softened
1 cup chopped toasted skinned hazelnuts