Brown the sausage in a nonstick pan over medium-high heat, breaking it apart. Halfway through, add onion and jalapeño. Cook until sausage is fully browned.
Remove 1 cup (180g) of the cooked sausage mixture and set aside.
Sprinkle flour over remaining sausage. Stir for 1 minute. Gradually whisk in milk. Simmer 5–8 minutes until thickened. Season with salt and pepper. Remove from heat.
Whisk eggs with salt. Melt butter in a pan over medium heat. Add eggs and scramble gently until just set. Remove from heat.
In a bowl, combine reserved sausage, scrambled eggs, cooked tater tots, and half of each cheese. Mix gently.
Preheat oven to 175°C (350°F). Lightly grease a 23×33 cm dish. Spoon ½ cup (120 ml) filling onto each tortilla, roll, and place seam-side down in dish.
Pour gravy over burritos. Top with remaining cheese.
Bake uncovered for 30–40 minutes, until cheese melts and edges bubble.