Preheat the oven to 375°F (190°C).
In a medium bowl, whisk together the eggs, whole milk, salt, and black pepper until fully combined.
Heat the olive oil in a large skillet over medium heat. Add the breakfast sausage and cook, breaking it apart 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, add the diced onion and jalapeño pepper. Cook for 3-4 minutes until softened.
Pour the egg mixture into the skillet with the onions and jalapeños. Cook over medium-low heat, stirring gently, until the eggs are softly scrambled and just set, about 3-4 minutes. Remove from heat and stir in the cooked sausage and 1 cup of shredded cheddar cheese.
Spread 1 cup of enchilada sauce evenly over the bottom of a 9×13 inch baking dish.
Warm the tortillas slightly to make them pliable, either in the microwave for 20 seconds or in a dry skillet for 10 seconds each side.
Divide the egg and sausage mixture evenly among the tortillas, placing the filling in the center of each. 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 1 cup cheddar cheese and 1 cup Monterey Jack cheese evenly on top of the enchiladas.
Bake in the preheated oven for 15-20 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let cool for 5 minutes. Garnish with chopped fresh cilantro before serving.