In the bowl of a stand-up mixer, whisk together the water, yeast, and a pinch of sugar. Let it rest for 5 minutes, until foamy. Add the browned butter, the warmed milk, 1/4 cup sugar, and egg.
Add 2 cups of flour, the salt, and baking powder. Beat on low speed, adding more flour (up to 1 1/2 to 2 cups more) until you have a soft, slightly sticky dough. Scrape down the sides of the bowl, sprinkle with a bit more flour, cover with plastic wrap, and let rest at room temperature for 30 minutes before placing in the refrigerator overnight.
In the morning, remove the dough from the refrigerator and let it sit at room temperature for 30 minutes.
Punch down the dough and dump it onto a lightly floured work surface. Roll the dough out into a roughly 16 x 12-inch rectangle and, using a pizza cutter, cut it into 2-inch squares. Cover lightly with plastic wrap.
In a medium saucepan fitted with a deep-fry thermometer and set over medium heat, heat about 2 inches of oil to 375 degrees F.
Spread a generous amount of powdered sugar (not the strawberry kind, we'll use that later!). Working in batches of about four, gently lower the beignets into the hot oil and cook for 2 to 3 minutes total, until golden brown on each side. Using a slotted spoon, transfer them directly to the powdered sugar and then dust them with the strawberry powdered sugar immediately. Let the oil return to 375 degrees before each batch and repeat with the remaining beignets. Serve immediately.