In a large mixing bowl, whisk together the flour, sugar, baking powder, cinnamon, nutmeg, and salt. In another bowl, beat the eggs and mix in the milk and vanilla extract. Melt the butter and let it cool slightly before adding it to the egg mixture. Combine both mixtures and stir until just combined.

Fry the Doughnuts

Heat oil in a deep fryer or a heavy pot to 375°F (190°C). Using a donut cutter or two round cutters, cut out doughnut shapes. Carefully place the doughnuts in the hot oil and fry until golden brown, about 2-3 minutes per side. Remove and place on paper towels to drain.

Coating and Serving

Dust with Spiced Sugar

In a shallow dish, mix together the granulated sugar, cinnamon, and nutmeg. While the doughnuts are still warm, roll them in the spiced sugar to coat evenly.

Serving

Serve the doughnuts warm with a scoop of vanilla gelato on top and drizzle with salted caramel sauce.