Special equipment: a deep-frying thermometer
1. Whisk the yeast into the warm milk in a large bowl and set aside until bubbly, 5 minutes. Add the sugar, oil, salt, egg and orange zest and whisk until well combined. Stir in 2 cups of the flour. Continue adding the remaining 1 cup flour, 1/2 cup at a time, until the dough is well combined.
2. Lightly flour a work surface. Lightly grease a large bowl with oil. Turn the dough out onto the floured surface and knead 10 to 12 times. Form the dough into a ball and place in the greased bowl. Set aside to rise until doubled in size, 45 minutes to an hour.
3. Heat 2 inches of oil in a heavy pot over medium heat until a deep-frying thermometer inserted in the oil registers 365 degrees F. Place a rimmed baking sheet lined with paper towels next to the stove. Put the confectioners' sugar in a paper bag.
4. Turn the dough out onto a lightly floured surface and roll out into a rectangle 1/4 inch thick. Cut out 24 squares of dough (2 inches by 2 inches) using a sharp knife. Add the squares to the hot oil in batches, about 8 per batch, and fry until golden brown, flipping as necessary, about 2 minutes per batch. Remove to the prepared baking sheet using a spider or a slotted spoon and allow to cool. In 2 to 3 batches, add the beignets to the paper bag with the sugar and shake to coat generously. Serve immediately.
Beignets are particularly good when served with the bitter chicory coffee that is famous in New Orleans. The bitter and the sweet are perfectly balanced.