Potato Doughnuts

Name: Potato Doughnuts
Ingredients: 1.4 ounces (40g; about 3 tablespoons) unsalted butter; 12 ounces russet potatoes (340g; about 2 medium potatoes), peeled and cut into 1-inch cubes; 12.5 ounces all-purpose flour (355g; about 2 3/4 cups), such as Gold Medal; 2 teaspoons (8g) baking powder; 1 teaspoon (4g) Diamond Crystal kosher salt; for table salt use half as much by volume or the same weight; 1/2 teaspoon baking soda; 1/2 teaspoon ground nutmeg; 4.6 ounces (130g; 2/3 cup) sugar; 2 large eggs (3 1/2 ounces; 100g); 2 ounces (55g; 1/4 cup) whole milk; 2 ounces (55g; 1/4 cup) cultured lowfat buttermilk, well-shaken; 1 1/2 teaspoons (7g) vanilla extract; Powdered sugar or cinnamon sugar, for dusting (see note); 2 quarts (1.9L) refined coconut oil, such as Nutiva, for frying