Combine Dry Ingredients: In a large mixing bowl, whisk together the all-purpose flour, nutmeg, sugar, and salt.
Prepare Wet Ingredients: Warm the milk and mix it with the egg, melted butter, and dry yeast. Let sit for 5 minutes to activate the yeast.
Mix Dough: Gradually combine the dry ingredients with the wet mixture. Stir until a dough forms.
Knead the Dough: Transfer the dough to a floured work surface and knead by hand for 10 minutes until smooth and elastic. Alternatively, use a stand mixer on high speed for 3 minutes.
First Rise: Place the dough in a greased bowl, cover with a kitchen towel, and allow it to rise in a warm area for 2 hours or until doubled in size.
Shape Donuts: Roll out the dough to 1/2-inch thickness. Use a round cutter to cut out donut shapes. Arrange on a baking tray lined with parchment paper.
Second Rise: Cover and let the donuts rise again for 30 minutes.
Fry Donuts: Heat oil in a deep pan to 160°C (320°F). Fry the donuts in batches until golden brown on both sides, about 1-2 minutes per side. Drain on paper towels.