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

In another bowl, mix the buttermilk, eggs, melted butter, and vanilla extract until well combined.

Gradually add the wet ingredients to the dry ingredients, stirring until just combined. Do not overmix.

Turn the dough out onto a floured surface and gently knead it a few times until it comes together.

Roll the dough to about 1/2 inch thick and cut into rectangles (about 3 inches by 1 inch).

In a deep skillet or fryer, heat about 2 inches of vegetable oil to 350°F.

Carefully add the donuts in batches, frying for about 2-3 minutes on each side or until golden brown.

Remove with a slotted spoon and drain on paper towels.

For the glaze, whisk together the powdered sugar, milk, and vanilla extract in a bowl until smooth.

Dip the warm donuts into the glaze, allowing any excess to drip off. Let the glaze set for a few minutes before serving.