Place water, butter, sugar, and salt in a sauce pan over medium high heat. Stir until butter is melted and everything comes to a boil.
Reduce heat to medium. Add flour into the mixture, stir to combine well with the butter mixture. Continue to stir and cook until the dough pulls away from the sides and starts to form into a ball, about 1 minute. Let cool for 5 minutes.
Using a hand mixer or stand mixer, beat the dough with the eggs, start with one egg until the egg is completely incorporated into the dough. Add the rest of the eggs, one at a time. Chill the dough in the refrigerator for one hour.
After chilling, shape the dough into small balls using a teaspoon or 1/2 tablespoon. Arrange the dough balls on a plate lined with parchment paper.
Heat 2-3 inches of oil in a frying pan on medium-low heat. When the oil is fully heated, drop the dough balls and fry them in batches.
Keep turning the dough balls around so they are evenly browned and puff up considerably.
The beignets are ready when they start to form a seam (the beignet will start to burst creating a seam when it is ready). Transfer out with a strainer and drain on paper towels. Sprinkle the powdered sugar generously and serve warm.