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 and cook, breaking it up with a spoon, 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 over medium-low heat, stirring gently, until the eggs are softly scrambled and just set, about 3-4 minutes. Remove from heat.
Stir the cooked sausage into the scrambled eggs.
Spread 1/2 cup of enchilada sauce evenly over the bottom of a 9×13 inch baking dish.
Warm the tortillas slightly to make them pliable, then spoon about 1/2 cup of the egg and sausage mixture onto the center of each tortilla.
Sprinkle about 2 tablespoons of shredded cheddar and Monterey Jack cheese over the filling in each tortilla.
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 in the preheated oven until the cheese is melted and bubbly, about 15 minutes.
Remove from the oven and let cool for 5 minutes.
Garnish with chopped fresh cilantro before serving.