In New Orleans, where I live, beignets are served with a snowstorm of powdered sugar. The puffy fried dough squares are sold at loads of places here, including the rightfully famous Café du Monde. (Insider tip: Café du Monde's location in City Park is even more magical than the well-traveled one in the French Quarter.) Anytime you order beignets to go, the paper bag is likewise loaded with powdered sugar. Capture that spirit by tossing these New Orleans–style beignets with powdered sugar in a large paper grocery bag. Or use a baking sheet coated with sugar. Whatever approach you choose, be sure to eat them while they’re piping hot. That’s half the point. The other half is finding yourself covered in white powder after a few bites.
Put the milk, yeast and 1 teaspoon of the granulated sugar in the bowl of a stand mixer fitted with the dough hook and mix on low to combine. Let sit until foamy, about 5 minutes.
Add the butter, salt, egg and remaining granulated sugar to the bowl and mix on low speed to combine. Add the flour in 1/2-cup increments, mixing on low speed just until the dough becomes sticky and pliable, about 2 minutes. Cover the bowl with plastic wrap and put somewhere warm to rise, such as inside an unlit oven, until the dough is roughly doubled in size, about 2 hours. (You can also refrigerate the covered dough overnight.)
Lightly flour a large work surface. Punch down the dough with your fist to remove air, then place the dough on the work surface. Roll the dough into a 12-by-14-inch rectangle that is about 1/4 inch thick. Make 6 cuts 2 inches apart along the 12-inch side and 7 cuts 2 inches apart along the 14-inch side using a sharp knife or pizza cutter for a total of forty-two 2-inch squares. Cover lightly with plastic wrap and let rest for at least 30 minutes. (If you refrigerated the dough, let the dough rest at least 1 hour.)
Heat the oil to 350 degrees F in a large Dutch oven or electric fryer. Put the confectioners' sugar in a large paper grocery bag or on a large baking sheet. Fry 6 to 8 beignets at a time, flipping them every 30 seconds or so, until both sides are golden brown, 2 1/2 to 3 minutes per batch. If using the paper bag, transfer the beignets to the bag and shake to coat well with the sugar. If using a baking sheet, transfer the beignets to the sheet and, using tongs, toss to coat well with the sugar. Repeat with the remaining dough. Serve immediately.
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