Prepare the Dough: In a large mixing bowl, combine 4 cups of all-purpose flour, ½ cup of granulated sugar, 2¼ teaspoons of instant yeast, ½ teaspoon of fine sea salt, and ¼ teaspoon of ground nutmeg. Mix these dry ingredients thoroughly before adding 1 cup of lukewarm whole milk, 1 large egg, ¼ cup of melted unsalted butter, and 1 teaspoon of vanilla extract. Stir until a smooth, sticky dough forms.

Knead the Dough: Transfer the dough to a lightly floured surface and knead for about 6-8 minutes using a stand mixer with a dough hook or 10 minutes by hand. You’ll know the dough is ready when it’s smooth and elastic, pulling away from the surface easily.

First Rise: Place the kneaded dough into a greased bowl, covering it with a clean kitchen towel. Let it rise in a warm environment for about 1.5 hours, or until it has doubled in size.

Shape the Doughnuts: Once risen, gently punch down the dough to release air, then roll it out on a floured surface to a thickness of about ½ inch. Use a doughnut cutter or two round cookie cutters to cut out your doughnut shapes.

Second Rise: Cover the shaped doughnuts with a towel once more and let them rise again for about 1 hour or until they have doubled in size.

Fry the Doughnuts: While waiting for the doughnuts to rise, heat vegetable oil in a deep skillet or fryer to 350°F. Carefully slide the doughnuts into the hot oil, frying them for about 1 minute on each side or until golden brown.

Prepare the Glaze: In a medium bowl, combine 2 cups of sifted powdered sugar, a pinch of fine sea salt, 1 teaspoon of vanilla extract, and ¼ cup of hot water. Whisk together until smooth and glossy.

Glaze the Doughnuts: Once the doughnuts are slightly cooled but still warm, dip the tops into the glaze, allowing any excess to drip back into the bowl.