Brown Butter Hazelnut Doughnuts

Ingredients

• 3/4 cup (168g) unsalted butter
• 3/4 cup (180g) buttermilk (110-115°F)
• 1 (0.25oz) package (7g) or 2 1/4 teaspoons Red Star Active Dry Yeast
• 2 teaspoons table salt
• 3 large eggs (lightly beaten, at room temperature)
• 1/2 cup (100g) light brown sugar
• 3 1/4 cups (455g) all-purpose flour
• 1 tablespoon granulated sugar
• 1 tablespoon hot water
• 1/2 cup (64g) hazelnuts
• 1 tablespoon turbinado sugar
• 1 tablespoon (14g) unsalted butter, melted
• 1 cup (120g) powdered sugar, sifted
• 1/8 teaspoon table salt
• 3 tablespoons Frangelico (hazelnut liquor)
• 3 tablespoons milk