Step 1: Heat olive oil in a large skillet over medium heat. Add the crumbled breakfast sausage and cook, breaking it apart with a spoon, until fully browned and cooked through. Drain any excess grease and set the sausage aside.
Step 2: In a medium bowl, whisk together the eggs, milk (or water), salt, and pepper until well combined and slightly frothy.
Step 3: Return the skillet (or use a fresh one) to medium-low heat. Pour in the egg mixture and cook, stirring gently with a spatula, until the eggs are set but still moist and fluffy. Be careful not to overcook.
Step 4: Warm the tortillas: You can do this in a dry skillet over medium heat for about 15-20 seconds per side, in the microwave for 15-30 seconds, or wrapped in foil in a warm oven.
Step 5: To assemble each roll-up, lay a warm tortilla flat. Spoon a portion of the scrambled eggs onto the center, followed by a portion of the cooked sausage. Sprinkle generously with shredded cheddar cheese.
Step 6: Fold in the sides of the tortilla, then tightly roll it up from the bottom. Serve immediately or prepare for meal prep.