In a mixing bowl, combine warm water and yeast. Let it sit for about 5 minutes until it becomes frothy. This step activates the yeast, ensuring your beignets will rise properly.

Add the granulated sugar, beaten egg, and evaporated milk to the yeast mixture. Whisk until well combined.

In a separate bowl, sift together the flour and salt. Gradually add the flour mixture to the wet ingredients, mixing until a soft dough forms.

Add the melted butter and knead the dough on a floured surface for about 5 minutes until smooth and elastic. This develops the gluten, giving the beignets their chewy texture.

Place the dough in a greased bowl, cover it with a clean kitchen towel, and let it rise in a warm place for about 1 hour, or until doubled in size.

Once the dough has risen, punch it down to release the air. Roll it out on a floured surface to about 1/4 inch thick.

Cut the dough into squares, approximately 2.5 inches by 2.5 inches. This is the traditional shape for beignets.

In a deep frying pan or fryer, heat the vegetable oil to 350°F (175°C). Use a thermometer for accuracy. If the oil is too hot, the beignets will burn; too cool, and they will absorb too much oil.

Carefully drop the dough squares into the hot oil, a few at a time, being careful not to overcrowd the pan. Fry for about 2-3 minutes on each side until golden brown.

Use a slotted spoon to remove the beignets from the oil and place them on paper towels to drain excess oil.

While the beignets are still warm, dust them generously with powdered sugar. Serve immediately for the best texture and flavor.