01 - Whisk together flour, yeast, sugar, and salt in a large mixing bowl until uniformly blended.
02 - In a separate bowl, whisk buttermilk, milk, eggs, and melted butter until smooth and fully incorporated.
03 - Create a well in the center of the dry ingredients. Pour the wet mixture into the well and stir with a wooden spoon until a shaggy, sticky dough forms.
04 - Turn dough onto a lightly floured surface. Knead firmly for 6–8 minutes, pushing forward with the heel of your hand and folding back, until the dough becomes smooth, elastic, and no longer sticky. Alternatively, use a stand mixer with a dough hook for 5 minutes on medium-low speed.
05 - Place dough in a lightly oiled bowl, turning once to coat all surfaces. Cover with plastic wrap or a damp towel and let rise in a warm, draft-free area for 60–75 minutes until doubled in bulk.
06 - Punch down the risen dough to release air. Turn onto a floured surface and roll to an even ½-inch thickness. Cut into 2-inch squares using a sharp knife or pastry cutter, pressing straight down without dragging.
07 - Arrange squares on a parchment-lined baking sheet, leaving space between pieces. Cover loosely with plastic wrap and let rest for 20 minutes until slightly puffy.
08 - Pour vegetable oil into a deep pot or Dutch oven to a depth of 3 inches. Heat over medium-high heat until the temperature reaches 350°F on a deep-fry thermometer. Maintain this temperature throughout frying.
09 - Carefully lower 4–5 dough squares into the hot oil using a slotted spoon. Fry for 1–2 minutes per side, flipping once, until deeply golden brown and puffed. Remove with a slotted spoon and drain on paper towels. Repeat with remaining squares.
10 - While beignets fry, whisk powdered sugar, milk, and vanilla extract in a medium bowl until completely smooth and lump-free. The glaze should be thick but pourable.
11 - Working while beignets are still warm, dip each square into the glaze, allowing excess to drip off briefly. Place glazed beignets on a wire rack set over parchment paper to set. Serve warm.