In a large mixing bowl, cream the 2 tablespoons unsalted butter, softened and 1 cup granulated sugar . Blend in 2 large eggs, beaten.
Sift or whisk 3 1/2 cups all-purpose flour, 2 teaspoons baking powder, 1/2 teaspoon salt, 1/4 teaspoon ground cinnamon and 1/4 teaspoon ground nutmeg in a separate bowl.
Add the dry ingredients alternately with the 3/4 cup sour milk, or buttermilk * see tips below on how to make your own sour milk.
Place dough in a medium-sized bowl, cover and chill for at least 2 hours.
Roll dough out onto a floured surface, about 1/3 inch thick and cut with doughnut or round/biscuit cutter. Reserve doughnut centers (holes).
Heat 24-48 oz. vegetable or canola oil to 350°F on a candy thermometer in a large stockpot or Dutch oven and fry doughnuts, 2-3 minutes on each side or until lightly golden brown. Be sure to have a well ventilated kitchen, or use ventilation fan when frying.
Using a slotted spoon or tongs, place doughnuts immediately on a wire rack lined with paper towels.
Repeat steps with remaining dough, until all dough has been used. Fry the remaining doughnut centers (holes) at the end, frying 1-2 minutes per side. Allow to drain and cool.
Combine glaze ingredients (4 cups powdered sugar, 1/2 cup milk, slightly warmed, 1 teaspoon vanilla extract , 1 tablespoon unsalted butter, softened ) in medium sized bowl; dip doughnuts and doughnut holes in glaze. Place on wire rack to allow glaze to harden completely before serving.