In a medium bowl, whisk together the eggs and milk until well combined. Season with salt and black pepper.
In a large skillet over medium heat, add the diced onion and bell pepper. Sauté for about 3-4 minutes until softened.
Add the cooked turkey sausage or chorizo to the skillet and cook for an additional 2 minutes, stirring occasionally.
Pour the egg mixture into the skillet and cook, stirring gently, until the eggs are fully cooked, about 3-5 minutes.
Remove the skillet from heat and stir in the black beans and shredded cheddar cheese until the cheese is melted.
Warm the tortillas in a separate skillet or microwave for about 15 seconds until pliable.
Spoon the egg mixture evenly onto each tortilla, then roll them up tightly to form burritos.
Serve with salsa and avocado slices, if desired.