Carnival Doughnuts

Name: Carnival Doughnuts
Ingredients: 4 cups plus 2 tablespoons unbleached pastry flour or unbleached all-purpose flour; 1 cup granulated sugar; ½ teaspoon baking soda; 2 teaspoons baking powder; ½ teaspoon kosher salt; 2 extra-large eggs; 2 cups buttermilk; 2 tablespoons mild-flavored honey, such as clover; 1½–2 tablespoons pure almond extract, to taste; 5–6 tablespoons orange flower water, to taste; Nonmelting icing sugar or powdered sugar; Pastry bag fitted with a #4 plain tip; Heavy-duty, deep saucepan filled halfway with vegetable oil