Stir together scalded milk, sugar, and salt in a large bowl; set aside to cool until tepid. Dissolve yeast in warm water in a small bowl; let stand until creamy, about 5 minutes.

Stir together flour and nutmeg in a bowl. Add 2 cups of flour mixture to the milk mixture; beat until well-blended.

Stir yeast mixture into milk and flour mixture, then mix in butter and eggs. Mix in remaining flour mixture, 1/2 cup at a time. When dough is firm enough, turn it onto a floured surface and knead for 3 to 4 minutes. Place into an oiled bowl, cover, and allow the dough to rise until doubled, 30 to 35 minutes.

Roll dough out on a lightly floured surface to 1/2-inch thickness. Cut into circles using a donut or round cutter. Set aside to rise until light, 30 to 40 minutes.

Heat 1-inch-deep oil in a deep, heavy frying pan to 375°F (190°C).

Fry donuts in hot oil a few at a time. Cook each side until golden brown, then remove to drain on paper towels. Glaze while warm or sprinkle with sugar.