In a small dish, combine the warm water, yeast, and sugar. Let the yeast sit for 10 minutes until it becomes frothy.
In a bowl, whisk together the gluten-free flour blend and salt. Add the yeast mixture, egg, coconut milk, and melted butter. Mix until a soft dough forms.
Cover the bowl with plastic wrap and let the dough rise for 45-60 minutes. To rise in an oven, preheat the oven to 200°F, turn it off, place the bowl inside, and leave the door cracked open.
After the dough has risen, remove the plastic wrap. Dust a piece of wax paper with gluten-free flour and roll the dough to ½ inch thickness. Cut the dough into small 1-inch squares using a sharp knife or pizza wheel.
Heat the oil in a Dutch oven or large cast iron skillet to 350°F. Fry the beignet squares in batches for 1 ½ minutes on each side, ensuring the oil is not too hot to avoid burning the outside while leaving the inside raw.
Remove the cooked beignets and place them on a paper towel to absorb excess oil. Toss the beignets in powdered sugar until well-coated.