Pour about 0.5-inch of vegetable oil into a large saute pan or pot and heat over medium heat to 355 degrees F. Keep an eye on the temperature as it heats up. Meanwhile, prepare the donut dough.

In a medium mixing bowl, whisk together the flour, 0.25 cup granulated sugar, baking powder, and salt.

In a separate bowl, whisk together the buttermilk and melted butter. Pour the buttermilk mixture into the flour mixture and, using a fork, stir until just combined. Be careful not to over-work the dough.

Roll the dough into approximately 0.5 Tbsp balls. Once the oil has reached 355 degrees F, fry about half of the dough balls at a time.

Fry until just golden brown on the bottom, then flip and cook the reverse side until also golden brown.

Carefully remove the fried donuts with a spider strainer or metal tongs and drain them onto a paper towel-lined baking sheet.

Pour the remaining 0.33 cup sugar into a shallow dish. Roll the warm donuts in the sugar to coat them. Repeat this process with the remaining dough and fried donuts.