In a large bowl, whisk together flour, baking powder, and salt. In a separate bowl, mix buttermilk and melted butter. Combine wet and dry ingredients just until a dough forms.

Turn dough onto a lightly floured surface and roll out to about 1/2-inch thickness. Use a donut cutter or a large round cutter with a smaller cutter to make holes.

Heat vegetable oil in a deep skillet over medium heat to 350°F. Fry the donuts in batches for approximately 2-3 minutes per side until golden brown.

Remove donuts and drain on paper towels. Toss in granulated sugar while still warm to coat evenly.