Heat a waffle iron according to the manufacturer’s instructions.
In a large bowl, using a wire whisk, combine the flour, cocoa powder, sugar, baking powder, baking soda, salt, and xanthan gum until well blended. Stir in the chocolate. Make a well in the center and set aside.
In a medium bowl, using a wire whisk, lightly beat the egg yolks. Gradually whisk in the melted butter until evenly combined. Whisk in the sour cream until well blended, then stir in the milk and vanilla extract. Set aside.
In a large bowl, using an electric mixer fitted with the whisk attachment or by hand using a wire balloon whisk, beat the egg whites just until stiff and the peaks hold their shape when the beater or whisk is lifted from the bowl.
Pour the liquid mixture into the well in the flour mixture all at once. Stir just until combined and the flour mixture is moistened. There may be a few small lumps; do not overmix. Add about 1 cup of the beaten egg whites to the batter and fold in to lighten the batter. Add the remaining egg whites and gently fold in just until blended.
Grease the heated waffle iron according to the manufacturer’s instructions. Spoon 3⁄4 cup to 1 cup of batter, or the amount recommended by the manufacturer, into the waffle iron. Use a heatproof spatula to spread the batter all the way to the edges. Bake until the indicator light signals the waffle is done or until the waffle is golden brown. Repeat with the remaining batter. Serve hot with your favorite syrup or topping.