Step #1 In a 10- to 12-inch nonstick frying pan over medium-high heat, onion, stir sausage, & chilies until meat is crumbled & browned, about 15 mins.
Step #2 Drain off & discard fat.
Step #3 In a bowl, 1/2 tsp salt, beat eggs to mix with 1/3 c water, & 1/2 tsp pepper.
Step #4 Pour eggs into meat mixture in frying pan; with a wide spatula, scraping pan bottom often, stir over medium-high heat, until eggs are set to your taste, about 3 mins for creamy eggs.
Step #5 Lay flour tortillas flat on a counter.
Step #6 Spoon an equal portion of the meat & egg mixture in a band down the center of each tortilla to within 1 inch of opposite edges.
Step #7 Sprinkle top mixture evenly with cheese.
Step #8 To form each burrito, fold the bare 1-inch-wide tortilla edges over filling, then roll snugly from an open edge to enclose.
Step #9 Set burritos slightly apart, seams down, in a 10- by 15-inch pan; seal pan with foil wrap.
Step #10 If making up to 1 day ahead, chill in the fridge.
Step #11 Bake in a 200° oven until cheese is melted (cut a slit to test), bake in a 325° oven until hot in the center, 15 to 20 mins; if chilled, about 15 mins.
Step #12 Set burritos on plates & ladle about 1/2 c hot chili con queso salsa on & around each.