Step 1: Prepare the Oil - In a deep frying pan or Dutch oven, heat 3 to 4 cups of vegetable oil over medium heat. Use a thermometer to check that the oil reaches about 350°F (175°C).
Step 2: Mix Dry Ingredients - In a mixing bowl, whisk together 1 1/4 cups of all-purpose flour, 2 teaspoons of baking powder, and 1/4 teaspoon of salt.
Step 3: Combine Wet Ingredients - In another bowl, mix 1/2 cup of buttermilk, 1/4 cup of granulated sugar, and 3 tablespoons of melted butter.
Step 4: Combine Mixtures - Pour the wet mixture into the dry mixture, stirring gently until just combined.
Step 5: Shape the Donuts - Using your hands or a small ice cream scoop, portion out the dough and shape it into small balls.
Step 6: Fry the Donuts - Once the oil is hot, carefully drop the shaped dough into the oil. Fry for about 1-2 minutes on each side until golden brown.
Step 7: Drain and Sugar Coat - Remove the donuts from the oil and place on a paper towel-lined plate. Roll in the remaining 1/3 cup of granulated sugar while warm.
Step 8: Serve and Enjoy! - Serve the donuts warm and enjoy!