01 - Whisk together flour, yeast, sugar, and salt in a large mixing bowl until thoroughly combined.
02 - In a separate bowl, blend buttermilk, milk, eggs, and melted butter until uniform.
03 - Create a well in the center of the dry ingredients. Pour in the wet mixture and stir until a shaggy, sticky dough forms.
04 - Turn dough onto a lightly floured surface. Knead for 6–8 minutes until smooth and elastic, or use a stand mixer with dough hook attachment for 5 minutes.
05 - Place dough in a lightly oiled bowl, cover with plastic wrap or a clean towel, and let rise in a warm, draft-free area for 60–75 minutes until doubled in volume.
06 - Punch down risen dough to release air. Roll out on a floured surface to approximately ½-inch thickness. Cut into 2-inch squares using a sharp knife or pastry cutter.
07 - Arrange squares on a parchment-lined baking sheet, cover loosely, and let rest for 20 minutes to puff slightly.
08 - Heat vegetable oil in a deep pot or Dutch oven to 350°F. Fry beignets in batches of 4–5, cooking 1–2 minutes per side until puffed and golden brown. Remove with a slotted spoon and drain on paper towels.
09 - While beignets fry, whisk powdered sugar, milk, and vanilla extract in a medium bowl until smooth and creamy.
10 - While beignets are still warm, dip each square into the glaze, allowing excess to drip off. Transfer to a wire rack set over parchment paper to set for 5 minutes before serving.