Whisk together the warm water, yeast, and a pinch of sugar in the bowl of a stand mixer. Let it rest for about 5 minutes, until it is foamy.
Add the butter, warm evaporated milk, 1/4 cup sugar, egg, and vanilla bean paste. Whisk to combine. Switch out the attachment to the dough hook.
Add 2 cups of flour, salt, and baking powder. Kneed on low speed and add more flour (up to about 1.5 cups more) until your dough comes together. It will still be slightly sticky (add more flour 1 Tablespoon at a time if it is too sticky). Scrape down the sides of the bowl and cover with plastic wrap. Let it rise in a warm environment for 1.5 hours.
Punch the dough and transfer to a lightly floured surface. Roll it out into a 16 X 12 inch rectangle. Use a pizza cutter to cut it into 2 inch squares. Lay a piece of plastic wrap over the sliced dough and let rest.
Meanwhile, heat oil in a large saucepan over medium heat. The oil needs to be about 2 inches deep. Use a candy thermometer to test the temperature of the oil. It is ready when it is 375 degrees F.
Set a drying rack over a rimmed baking pan and set to the side of the pan (you will place beignets on this after frying for dusting).
Gently lower about 4 of the beignet squares into the pot with hot oil. Let them cook for about 30 seconds-1 minute and then use a frying spoon (called a spider) to flip the beignet over. Cook for about 1 minute longer. They should be golden brown on each side. Use the spoon to remove the beignet from the fryer and transfer to the wire rack. Sift powdered sugar over the beignets and serve immediately.
Repeat with remaining squares, making sure that the oil returns to 375 before each batch. Enjoy!