In a small bowl, stir together ½ cup (120 grams) warm water, yeast, and 1 teaspoon (4 grams) granulated sugar. Let stand until foamy, about 5 minutes.

In the bowl of a stand mixer, whisk together ½ cup (120 grams) boiling water, evaporated milk, melted butter, salt, vanilla, and remaining ¼ cup (50 grams) granulated sugar by hand. Whisk in yeast mixture and egg. Add flour. Using the dough hook attachment, beat until dough comes together, starts to get smooth and soft, and forms a ball at base of dough hook, 6 to 7 minutes, stopping to scrape sides of bowl. (Dough should stick to your fingers when you touch it but release after you pull away. Dough will still stick to bottom and sides of bowl.) Check dough for proper gluten development using the windowpane test. (See Beignet Dough Basics.)

Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and refrigerate for at least 2 hours or up to overnight.

In a large Dutch oven, pour oil to a depth of 2 inches, and heat over medium heat until a deep-fry thermometer registers 375°F (190°C). (See Note.)

Divide dough in half (about 518 grams each). On a heavily floured surface, roll half of dough into a 13×10-inch rectangle (about ¼ inch thick). (Cover and refrigerate remaining dough.) Trim ½ inch of edges so rectangle is 12×9 inches. Cut into 3-inch squares, and separate them so they do not stick back together.

Place 2 to 3 squares in hot oil; when settled on top of oil, immediately turn. (See Frying 411 on page 40.) Fry until golden brown, about 1 minute per side. Carefully remove from hot oil, and let drain on paper towels. Repeat procedure with remaining dough. Sift confectioners’ sugar over hot beignets. Serve warm.