Add the warm water, active yeast, and 1 tbsp sugar and whisk until combined. Let sit for 7-10 minutes until it forms a raft on top.
Next, pour in the remaining sugar, whole milk, eggs, and melted unsalted butter and whisk until combined.
Add in the salt and all purpose flour and either knead or mix on medium speed until smooth and the dough has pulled away from the inside of the bowl, about 2-3 minutes.
Cover the dough with plastic wrap or a towel and let sit at room temperature until it has doubled in size, about 90 minutes.
Move the dough to a large clean surface dusted with flour and roll out until it is ¾ inches thick and cut into 1½ x 3 inch rectangles. You may need to add more flour if the dough is too sticky.
Add several of the beignets to a pot with neutral oil for frying or a deep fryer set to 350°F and cook each side is until golden brown. This will only take a minute or so for each side.
Cook in batches until the beignets have all been deep friedand set on a sheet tray with paper towels and drain.
Roll the beignet in powdered sugar and serve.