01 - Whisk together flour, yeast, sugar, and salt in a large mixing bowl until thoroughly combined.
02 - In a separate bowl, blend buttermilk, whole milk, eggs, and cooled melted butter until smooth.
03 - Create a well in the center of the dry ingredients. Pour the wet mixture into the well and stir until a shaggy, sticky dough forms.
04 - Turn dough onto a floured surface and knead for 6–8 minutes until smooth and elastic. Alternatively, use a stand mixer with dough hook for 5 minutes on medium-low speed.
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 size.
06 - Punch down the risen dough to release air. 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 until slightly puffed.
08 - Heat vegetable oil in a deep pot or Dutch oven to 350°F. Fry beignets in batches, cooking 1–2 minutes per side until golden brown and puffed. Remove with a slotted spoon and drain on paper towels.
09 - Whisk powdered sugar, milk, and vanilla extract in a bowl until completely smooth and lump-free.
10 - While beignets are still warm, dip each square into the glaze, allowing excess to drip off. Place on a wire rack to set for 5 minutes before serving.