Combine the warm water, about 2 tablespoons of the sugar, and yeast in a large bowl and let sit for 5-10 minutes until the yeast is foamy.
Add the remaining sugar, milk, butter, salt, egg, and 2 cups of the flour, mixing until well-combined using the paddle attachment of a stand mixer. Add the remaining flour, kneading until it comes together into a soft dough, about 1-2 minutes.
Transfer the dough to a lightly greased bowl, turning to coat, then cover with plastic wrap and let rise until doubled in size, or refrigerate overnight.
Roll out onto a lightly floured surface until about ¼-inch thick. Cut into 2"x3" rectangles using a pizza cutter.
Heat the oil in a large skillet over medium-high heat to 375 degrees F. Fry the beignets for 1 ½ to 2 minutes, flipping partway through, until crispy and golden brown on the outside. You will need to work in batches with a few beignets at a time so as not to crowd the pan and drop the oil temperature too much.
Transfer the cooked beignets to a baking sheet lined with a wire rack to drain as they finish. Dust with a generous coating of powdered sugar before serving warm.