Using a thermometer, get water to a warm 105-110 degrees.Once in that ranges, sprinkle the envelope of yeast into the water and gently stir.
Let the yeast bloom. This will take about 5 minutes or so, you will see the yeast bubble up and bloom.Tap the cup on the counter to agitate the water slightly to get it going if desired.
Meanwhile, combine sugar, salt and flour in a large bowl. Combine the milk, egg, vanilla and melted butter in a separate bowl. Once the yeast has bloomed, stir the yeast water and add it to the wet ingredients. Add this to the flour mixture and mix with your hands until a wet dough forms. Once together, lightly knead for 3-5 minutes, sprinkling a little flour over the dough if it becomes too sticky. Once the dopugh is soft and satiny, cover the bowl with a towel and let it rest/rise for one hour.
Heat the oil to 350-365 degrees.
Using a rolling pin, roll out the dough a small bit at a time to a fairly thin dough. Using a pizza wheel cutter, cut into 2" x 2" squares. Place 4 squares into the oil at a time, turning the suares in the oil when lightly browned on one side - after about 20 seconds or so. Remove with a slotted spoon when lightly browned and puffed all over. This goes fast so don't leave this station until finished.
Toss the four beignets in a paper bag with powdered sugar for serving. If making lemon beignets, take the beignets out of the bag after tossing in sugar and place on a plate. Zest lemon peel on top of the beignets and serve..
Working in batches of four at a time, continue to use separate bags for each order. Let your guests do the shaking to make it more fun!
The less handled the dough is, the softer the beignet. Rolling to the correct thickness is also important. Watch the beignets carefully while they are frying - Do not over cook. You can sprinkle with cinnamon sugar also.