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.
NotesCook's Note: 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.