Cook the bacon in a skillet over medium heat until crisp; drain on paper towels.
Whisk the beaten eggs with milk, salt, and pepper in a medium bowl.
Melt the butter in a nonstick skillet over medium-low heat. Scramble the eggs gently until just set, then remove from heat.
Warm the tortillas in a dry skillet or microwave until pliable.
Fill each tortilla with cheese, scrambled eggs, crumbled bacon, and green onions. Roll tightly, tucking in the sides.
Toast the wraps seam-side down in the skillet for 1–2 minutes to seal. Slice and serve with salsa.