Proof the Yeast:
* In a small bowl, combine the 1/4 cup of warm water (105-115°F / 40-46°C) with a pinch of the granulated sugar.
* Sprinkle the 2 1/4 teaspoons of active dry yeast over the water.
* Let it stand for 5-10 minutes until the mixture is foamy and bubbly. This indicates the yeast is active. If it doesn’t foam, your yeast may be old, and you’ll need to start over with fresh yeast.

2. Combine Wet Ingredients:
* In the large bowl of a stand mixer fitted with the dough hook attachment (or a large mixing bowl if making by hand), combine the remaining 1/4 cup of granulated sugar, the 3/4 cup of warmed evaporated milk, the lightly beaten egg, the 1/2 teaspoon of salt, and the 2 tablespoons of melted butter (and vanilla extract, if using).
* Once the yeast mixture is foamy, add it to the wet ingredients in the bowl. Stir briefly to combine.

3. Add Flour and Mix the Dough:
* Gradually add 3 1/2 cups of the all-purpose flour to the wet ingredients.
* Using a Stand Mixer: Mix on low speed until the flour is incorporated and a shaggy dough begins to form. Increase the speed to medium-low and knead for 5-7 minutes. The dough should become smooth, elastic, and pull away from the sides of the bowl, though it will still be slightly sticky to the touch. If the dough is overly sticky after a few minutes of kneading, add the remaining 1/2 cup of flour, a tablespoon at a time, until it reaches the desired consistency.
* Making by Hand: If mixing by hand, stir the flour into the wet ingredients with a wooden spoon until a shaggy dough forms. Turn the dough out onto a lightly floured surface and knead for 8-10 minutes until smooth and elastic. Add more flour sparingly as needed to prevent sticking.

4. First Rise (Bulk Fermentation):
* Lightly grease a large bowl with oil or cooking spray.
* Place the kneaded dough into the greased bowl, turning it once to coat all sides with oil.
* Cover the bowl tightly with plastic wrap or a clean kitchen towel.
* Let the dough rise in a warm, draft-free place for 1.5 to 2 hours, or until it has doubled in size. The exact time will depend on the temperature of your kitchen.

5. Roll and Cut the Dough:
* Once the dough has doubled, gently punch it down to release the air.
* Turn the dough out onto a well-floured work surface. The dough will be soft.
* Using a lightly floured rolling pin, roll the dough out into a rectangle approximately 1/4 to 1/3-inch thick. Try to keep the thickness even.
* Using a sharp knife or a pizza cutter, cut the dough into 2.5 to 3-inch squares or rectangles. You can also cut them into diamond shapes if you prefer. Don’t worry if they aren’t perfectly uniform; irregularity is part of their charm. You should get about 18-24 beignets.

6. Prepare for Frying (Optional Second Rise):
* Lightly flour a baking sheet. Place the cut beignet pieces on the floured baking sheet, ensuring they don’t touch.
* Cover them loosely with a kitchen towel and let them rest for another 15-30 minutes while you heat the oil. This short rest can help them puff up more dramatically. This step is optional; some fry immediately after cutting.

7. Heat the Frying Oil:
* Pour your chosen frying oil into a large, heavy-bottomed pot (like a Dutch oven) or a deep fryer to a depth of at least 2-3 inches.
* Heat the oil over medium-high heat until it reaches a temperature of 360-370°F (182-188°C). Use a deep-fry thermometer or candy thermometer to monitor the temperature accurately. If the oil is too cool, the beignets will absorb too much oil and be greasy. If it’s too hot, they will brown too quickly on the outside before the inside is cooked.

8. Fry the Beignets:
* Carefully place 3-4 pieces of dough into the hot oil at a time, being sure not to overcrowd the pot. They will puff up almost immediately.
* Fry for about 1-2 minutes per side, or until they are beautifully golden brown and puffy. They cook very quickly. Use tongs or a slotted spoon to gently turn them as they fry to ensure even browning.
* Once golden brown on both sides, use a spider skimmer or slotted spoon to remove the beignets from the oil, allowing any excess oil to drip back into the pot.

9. Drain and Dust with Powdered Sugar:
* Immediately transfer the hot, fried beignets to a wire rack lined with paper towels to drain briefly.
* While the beignets are still very warm, generously (and I mean generously) dust them with powdered sugar. The traditional way is to place them in a paper bag with a good amount of powdered sugar and shake gently to coat, or use a fine-mesh sieve to shower them from above. Don’t be shy!

10. Serve Immediately:
* Beignets are best enjoyed fresh and warm, within minutes of being fried.
* Serve with a hot cup of café au lait (coffee with chicory and hot milk) for the truly authentic New Orleans experience.