Apple Cider Doughnut Cake Recipe

Name: Apple Cider Doughnut Cake Recipe
Ingredients: 9 tablespoons (4 1/2 ounces) unsalted butter, at room temperature; 1 large Granny Smith apple (about 8 ounces), peeled, cored, and roughly chopped; 1 1/2 cups apple cider; 1/2 cup milk, at room temperature; 2 1/2 cups (about 12 1/2 ounces) all-purpose flour; 1 1/2 teaspoons baking powder; 1/2 teaspoon baking soda; 1 teaspoon salt; 1/4 teaspoon ground nutmeg; 1/4 teaspoon ground mace; 3/4 cup (about 5 1/4 ounces) sugar; 1/2 cup (about 3 1/2 ounces) packed light brown sugar; 3 large eggs, at room temperature; 1/4 cup vegetable oil; 1 teaspoon pure vanilla extract; 6 tablespoons granulated sugar; 1 teaspoon ground cinnamon; 1/8 teaspoon ground nutmeg; 1/8 teaspoon salt