Step 1

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.

Step 2

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.)

Step 3

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.)

Step 4

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.