Heat 1 tablespoon olive oil in a 12-inch nonstick skillet over medium heat. Add the diced onion and bell pepper and cook for 4 to 5 minutes until softened.
Add the turkey sausage to the skillet, breaking it into small pieces with a spoon. Cook for 6 to 7 minutes, stirring occasionally, until no longer pink and an instant-read thermometer reads 165 F / 74 C.
Drain any excess fat from the skillet. Stir in the cumin, smoked paprika and black beans, and cook for 2 minutes until warmed through. Transfer the mixture to a bowl.
Whisk the eggs, milk, salt and pepper together in a mixing bowl. Wipe out the skillet and set it back over medium-low heat.
Pour the eggs into the skillet. Stir gently every 30 seconds and cook for 3 to 4 minutes until softly set with small, glossy curds. Pull the pan while the eggs still look a touch underdone, since they'll finish cooking when the burritos get reheated.
Fold the eggs into the sausage and bean mixture. Sprinkle in the cheddar and stir until it just starts to melt.
Warm the tortillas one at a time in a dry skillet or over a low gas flame for 10 to 15 seconds per side, until pliable.
Lay a tortilla flat and spoon about 1 cup (230 g) of filling onto the lower third. Fold in the sides and roll tightly into a burrito. Repeat with the remaining tortillas.
To eat right away, serve warm with salsa. To freeze, let the assembled burritos cool at room temperature for about 15 minutes so condensation doesn't turn the tortilla soggy.
Wrap each burrito individually in foil, then set them on a sheet pan and freeze until solid, about 2 hours.
Transfer the frozen, wrapped burritos to a freezer bag or airtight container. Freeze for up to 3 months.