In a large bowl, whisk together the flour, granulated sugar, baking powder, salt, and nutmeg.

In a separate bowl, whisk the milk, eggs, melted butter, and vanilla until well combined.

Pour the wet ingredients into the dry ingredients and stir just until a soft dough forms. Do not overmix.

Lightly flour a work surface and turn out the dough. Pat it to about 1/2-inch thickness.

Cut the dough into rounds using a doughnut cutter or two different-sized round cutters.

Heat 2 to 3 inches of vegetable oil in a heavy pot to 350 degrees F.

Fry the doughnuts in batches for about 1 to 2 minutes per side, until golden brown and cooked through.

Transfer the doughnuts to a paper towel-lined plate to drain briefly.

While still warm, toss the doughnuts in powdered sugar until fully coated.

Serve fresh for a sweet baseball snack.