In a medium bowl, whisk together water, sugar, and yeast. Let sit for 5-10 minutes or until foamy. Once foamy, add milk and egg. Whisk to combine. Set aside.
To the bowl of a stand mixer fitted with a dough hook, add flour and salt. With the mixer on low, add the yeast mixture and butter. Mix until just combined.
Increase speed to medium and continue kneading for 2-3 minutes, or until dough is smooth and cleans the sides of the bowl.
To a large bowl that has been sprayed with non-stick cooking spray, add the dough. Cover and let rise until doubled, about 1-2 hours.
Once the dough has doubled roll it out into a rectangle about ¼ - ½-inch thick onto a lightly floured surface. Using a pizza cutter, cut the dough into 32 squares. First, cut the dough horizontally into 4 sections, then vertically into 8 sections.
In a large pot over medium heat, using a thermometer, heat about 3 inches of oil to 360°F. Working in batches, carefully place 4-6 pieces of dough into the hot oil, making sure to not overcrowd the pan. Cook for about 30 seconds to a minute on each side, or until golden brown. Place the fried beignets on a paper-towel-lined baking sheet and dust with confectioners' sugar.
Repeat with the remaining dough, making sure the oil temperature is back at 360°F before making the next batch.