In a small bowl, mix warm water, yeast, and a pinch of sugar. Let sit for 5–10 minutes until the mixture becomes foamy and bubbly.

In a large mixing bowl, whisk together the sugar, eggs, milk, melted butter, and vanilla extract.

Gradually add flour and a pinch of salt to the wet mixture, stirring continuously. Knead the dough by hand or with a dough hook for 5–7 minutes, until smooth and elastic.

Place the dough in a greased bowl. Cover and let it rise in a warm area for 1–2 hours, or until doubled in size.

On a lightly floured surface, roll out the dough to about ½-inch thickness. Cut the dough into 2-inch squares or desired shapes.

In a deep pot or deep fryer, heat oil to 350°F (175°C). Use a thermometer to maintain the correct frying temperature.

Carefully lower a few dough squares into the hot oil without overcrowding. Fry for 2–3 minutes per side, or until golden brown and puffed.

Use a slotted spoon to transfer the beignets to a paper towel-lined plate to drain excess oil.

Let beignets cool slightly, then generously dust with powdered sugar. Serve warm.