01 - Whisk together flour, yeast, sugar, and salt in a large mixing bowl until thoroughly blended.
02 - In a separate bowl, whisk buttermilk, milk, eggs, and melted butter until uniform.
03 - Create a well in the dry ingredients. Pour in the wet mixture and stir with a wooden spoon until a shaggy, sticky dough forms.
04 - Turn dough onto a floured surface and knead for 6–8 minutes until smooth and elastic, or use a stand mixer with dough hook for 5 minutes.
05 - Place dough in a lightly oiled bowl, cover with plastic wrap or a damp towel, and let rise in a warm, draft-free area for 60–75 minutes until doubled in size.
06 - Punch down risen dough. Roll out on a floured surface to 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 with a towel, and let rest for 20 minutes.
08 - Pour vegetable oil into a deep pot or Dutch oven. Heat to 350°F, monitoring with a deep-fry thermometer.
09 - 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.
10 - While beignets fry, whisk powdered sugar, milk, and vanilla extract in a medium bowl until smooth and lump-free.
11 - Dip warm beignets into the glaze, allowing excess to drip off. Place on a wire rack set over parchment paper to set for 5 minutes before serving.