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Melt butter over medium heat in a medium-sized saucepan, stirring often, until butter foams and then browns (do not burn), 5 - 8 minutes. Transfer to a mixing bowl and let cool.
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Whisk milk, buttermilk, sugar, yeast, and salt in a large mixing bowl. Whisk in flour and cooled brown butter.
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Cover and let batter sit at room temperature at least 8 hours and up to 12 hours.
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Once the 8 hours is up, whisk in eggs and baking soda.
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Heat waffle iron until very hot. coat iron with nonstick spray and pour batter onto waffle iron, spreading it to cover surface. Cook until golden brown and cooked through.
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Serve immediately with butter and maple syrup.