In a stand mixer fitted with a dough hook, combine the sourdough starter, flour, granulated sugar, buttermilk, melted butter, and salt.
Knead on low speed for about 5 minutes until fully combined and smooth. The dough should form a nice ball but still be slightly sticky.
Cover the dough and let rest at room temperature for 4-6 hours or until doubled in size. Place the bowl in the fridge and let the dough continue to ferment overnight (or up to 48 hours).
When you're ready to make the beignets, heat about 2 inches of canola oil over medium-high heat in a large skillet or dutch oven. It should take 5-10 minutes for the oil to heat to 350°F.
Lightly flour the countertop and roll out the dough into a large rectangle, about ¼ inch thick. Then cut the dough into 3 inch squares.
Fry 3-5 beignets at a time, making sure not to crowd the pan. Flip the dough often until they are puffed and golden brown on each side.
Transfer to a cooling rack for about 2 minutes to drain off the excess oil.
Dust very generously with powdered sugar and enjoy while still warm!
Notes
The beignets are best eaten the same day but they will keep in an airtight container at room temperature for up to 2 days.