Apple Cider Doughnuts with Pumpkin Spice Glaze

Name: Apple Cider Doughnuts with Pumpkin Spice Glaze
Ingredients: 3 1/3 cups apple cider; 3 1/2 cups all-purpose flour, plus more for shaping; 2/3 cup firmly packed light brown sugar; 2 teaspoons baking powder; 1/2 teaspoon baking soda; 1 teaspoon ground cinnamon; 1 teaspoon kosher salt (see Cook’s Note); 1/4 teaspoon ground nutmeg; 2 large eggs, lightly beaten; 6 tablespoons unsalted butter, melted and cooled; 1 teaspoon vanilla extract; Canola oil, for frying; 2 cups powdered sugar; 1/2 teaspoon pumpkin pie spice; Large pinch kosher salt