In a small bowl, whisk eggs with milk, salt, and pepper until frothy.
Cook sausage in a skillet over medium heat, breaking it into crumbles, until browned and cooked through (about 5 minutes). Transfer to a plate and drain excess fat.
In the same skillet, melt butter over medium-low heat. Add egg mixture and cook, stirring gently, until soft curds form (about 3-4 minutes). Remove from heat.
Warm tortillas in a dry skillet or microwave until pliable.
Divide scrambled eggs among tortillas, placing in a line down the center. Top with sausage, cheese, salsa, sour cream, and cilantro if using.
Fold in the sides, then roll up tightly from the bottom to enclose filling. Serve immediately.
Tips
For extra flavor, add diced jalapeño or hot sauce.
To make ahead, wrap burritos in foil and refrigerate; reheat in a skillet or oven.
Substitute turkey sausage or vegetarian sausage for a lighter version.