Dissolve yeast in warm water in a large mixing bowl. Add milk and next 5 ingredients. Vigorously beat in flour. Dough will be very sticky.
Work a fourth of the dough at a time. Place dough on a heavily floured surface. Use a well-floured rolling pin to roll dough to about 1/8-inch thickness. Cut into 2-inch squares. Drop beignets, a few at a time, into 370 degree oil. As beignets rise to the surface and puff, turn over to brown other side. When uniformly browned, remove from oil and drain on paper towels.