Preheat the oven to 375°F (190°C).
In a medium bowl, whisk together the eggs, whole milk, salt, and black pepper until well combined.
Heat the olive oil in a large skillet over medium heat. Add the breakfast sausage, breaking it apart with a spatula, and cook until browned and cooked through, about 6-8 minutes. Remove the sausage from the skillet and set aside.
In the same skillet, pour in the egg mixture and cook, stirring gently, until the eggs are softly scrambled and just set, about 3-4 minutes. Remove from heat.
Add the cooked sausage back to the scrambled eggs and stir to combine.
Spread 1/2 cup of enchilada sauce evenly in the bottom of a 9×13-inch baking dish.
Warm the tortillas slightly in the microwave or on a skillet until pliable.
Place about 1/4 cup of the egg and sausage mixture down the center of each tortilla. Sprinkle with a total of 1/2 cup shredded cheddar and Monterey Jack cheese evenly divided among the tortillas.
Roll up each tortilla tightly and place seam-side down in the prepared baking dish.
Pour the remaining enchilada sauce evenly over the rolled tortillas.
Sprinkle the remaining shredded cheddar and Monterey Jack cheese evenly over the top.
Bake uncovered in the preheated oven for 15 minutes, or until the cheese is melted and bubbly.
Remove from the oven and garnish with chopped fresh cilantro before serving.