Heat 2 inches (in depth) of oil over medium-high heat in a large, heavy pan.
Unroll the crescent dough and pull the triangles apart on the dotted line. Cut each triangle in half to make two small triangles.
Gently place a few pieces of dough at a time into the hot oil. Fry for 2 to 3 minutes, turning occasionally with a slotted spoon, until golden brown all over.
Remove beignets from oil and place on a plate covered with paper towels to drain.
Place one cup of sugar in a brown lunch bag and add a few beignets at a time. Close the top and shake the bag to cover the beignets in sugar. This is a good step for the kids to do!
Remove from the bag and serve warm.