Preheat a deep-fryer, deep pot, or Dutch oven with at least 3 inches of oil to 375ºF. Lay a couple of plates out, lined with at least 3 paper towels each; set aside.
Make the pate a choux dough in the above cream puffs recipe but do not place it in a piping bag nor bake them.
Once the oil is hot enough, using a 1-1/2-inch wide cookie or ice cream spring-action scooper, add 3 to 4 round scoops of dough to the oil. Alternatively, use two serving tablespoons, one to scoop up the dough and the other to scrape the dough off of the other spoon. Leave lots of room for them to expand to double their size. (If you overcrowd the oil they will not brown well and will turn out very greasy as the temperature of the oil drops from all of the cold dough.) Fry for 7 minutes, flipping, rolling, and dunking the dough often to brown evenly.
Using a slotted spoon or spider spatula, remove the beignets from the oil and allow excess oil to drip back into the pot or deep-fryer. Transfer to the paper-towel-lined plates to drain for 2 minutes.
Dust the beignets that you plan on serving immediately with confectioners' sugar. If you have leftovers, allow them to remain at room temperature, covered with paper towels, or store in a paper bag. Do not seal them in an air-tight container unless you place some paper towels in the container to absorb any moisture. It's really best to leave them out at room temperature to dry. Then dust with confectioners' sugar before serving.