Whisk eggs, milk, salt, and pepper in a bowl.
Melt butter in a large skillet over medium; add eggs and scramble gently about 5 minutes until just set.
Warm tortillas in microwave 20-30 seconds or in a dry skillet until pliable.
Divide eggs evenly among four tortilla centers.
Top with sausage, crispy hash browns, cheese, salsa, and optional sour cream.
Fold sides in; roll tightly from bottom to enclose filling.
Optional: toast burritos seam-side down in a hot skillet 1-2 minutes to seal.
Serve immediately with extra salsa.