Apple Cider Donuts

Name: Apple Cider Donuts
Ingredients: 2 1/2 cups apple cider or unfiltered apple juice; 6 tablespoons unsalted butter; 3 1/2 cups all-purpose flour, plus more for dusting; 3 teaspoons ground cinnamon, divided; 2 or 4 teaspoons baking powder (see Recipe Instructions); 1 teaspoon kosher salt; 1/2 teaspoon baking soda; 1/2 teaspoon ground nutmeg, preferably freshly grated; 1/2 cup packed light or dark brown sugar; 1/2 cup unsweetened applesauce; 1/3 cup cold buttermilk or kefir; 2 cold large eggs; 1 cup granulated sugar; 2 quarts vegetable, canola, or peanut oil, for deep frying