Add the warm water, yeast and 1 tablespoon of sugar to a standing mixer bowl and whisk until combined. Let sit for 7-10 minutes until it forms a raft on top.
Next, pour in the remaining sugar, milk, eggs, and melted butter and whisk until combined.
Attach the bowl the stand mixer with the hook attachment and add in the salt and flour and 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.
Transfer the dough to a large clean surface dusted with flour and roll out until it is ½” to ¾” thick and cut into 1 ½” to 2” squares or rectangles.
Add 5-6 of the beignets to a pot with hot oil or a deep fryer set to 350° and cook for 1 1 1/2-2 minutes per side or until golden brown.
Cook in batches until the beignets have all been fried and set on a sheet tray lined with parchment paper or paper towels and drain.