Pour enough vegetable oil into a deep pot to reach a depth of about three inches and heat to 365°F.

In a large mixing bowl, whisk together all-purpose flour, granulated sugar, baking powder, and salt.

In a separate bowl, mix buttermilk, pure vanilla extract, and melted butter until smooth.

Gently pour the wet ingredients into the dry ingredients and mix until just combined, leaving it slightly lumpy.

Turn the dough onto a floured surface and roll it out to about ½ inch thick, then cut out donut shapes.

Carefully lower the formed donuts into the preheated oil, frying no more than three at a time for about 2 minutes on each side.

While warm, roll each donut in granulated sugar to coat thoroughly, and let cool on a wire rack.