Cook the Sausage:
If using sausage links, cook them in a skillet over medium heat until browned and cooked through, about 8–10 minutes. For ground sausage, cook and crumble in the skillet until fully browned. Remove from skillet and set aside.

Prepare the Eggs:
In a medium bowl, whisk together eggs, milk, salt, and pepper until fully combined.

Scramble the Eggs:
In the same skillet, melt the butter over medium heat. Pour in the egg mixture and cook gently, stirring occasionally, until the eggs are softly scrambled. Remove from heat.

Assemble the Wraps:
Warm the tortillas briefly in the microwave or in a dry skillet until flexible. Place an equal portion of scrambled eggs in the center of each tortilla. Top with cooked sausage and sprinkle with shredded cheese. Fold the sides in, then roll up the tortilla tightly to form a wrap.

Heat and Serve:
For a crispy finish and melted cheese, lightly toast the wraps in a skillet or grill pan over medium heat for 1–2 minutes on each side. Serve immediately with optional salsa, hot sauce, or green onions.