Fry the sausage in a medium skillet. Spoon the cooked sausage onto a paper towel-lined plate to drain, reserving the grease.
Scramble the eggs and fry them in the remaining sausage grease.
As the eggs are frying, prepare the sausage gravy according to package instructions.
Grill the hot dogs.
To assemble, spoon sausage gravy into each potato roll, nestle a hot dog on top of the gravy, then top with crumbled sausage, scrambled eggs, and chives.