Preheat oven to 300°. Heat waffle iron until very hot. Whisk flour, sugar, baking powder, baking soda, and kosher salt in a large bowl. Using an electric mixer, beat egg whites in a medium bowl until medium-soft peaks form. Whisk egg yolks, melted butter, buttermilk, and soda water in a medium bowl; gradually whisk into dry ingredients. Fold in egg whites.
Coat waffle iron with non-stick vegetable oil spray. Pour batter onto iron, spreading it into corners (amount of batter needed will vary according to machine). Scatter 1 rounded Tbsp. ham and 1 Tbsp. white cheddar over each waffle. Cook until golden brown and cooked through. Transfer to a baking sheet; keep waffles warm in oven between batches. Serve with butter and warm maple syrup.