Heat a large skillet over medium-high heat. Add the breakfast sausage, breaking it into crumbles as it cooks. Cook until no longer pink, about 5-7 minutes.
Transfer the cooked sausage to a paper towel-lined plate to drain, reserving about 1 tablespoon of fat in the skillet.
In the same skillet, add the diced bell pepper and onion. Cook until softened, about 4-5 minutes. Add the garlic and cook for another 30 seconds until fragrant.
If using hash browns, add them to the vegetable mixture and cook until they begin to crisp up, about 3-4 minutes.
Return the sausage to the skillet along with the green chilies (if using). Stir to combine everything.
In a mixing bowl, whisk together the eggs, milk, salt, pepper, and cumin until well combined.
Push the sausage and vegetable mixture to one side of the skillet. Add the butter to the empty side and let it melt.
Pour the egg mixture into the buttered side of the skillet. Cook, gently stirring and folding the eggs, until they are just set but still slightly moist, about 3-4 minutes.
Combine the eggs with the sausage mixture in the skillet. Remove from heat and stir in 1 1/2 cups of the shredded cheese and cilantro (if using) until the cheese begins to melt.
Allow the filling to cool slightly before assembling the burritos. This prevents the tortillas from becoming soggy.
Warm the tortillas by placing them one at a time in a dry skillet for about 10 seconds per side, or wrapping the stack in damp paper towels and microwaving for 30 seconds.
Assemble the burritos by placing about 2/3 cup of filling slightly off-center on each tortilla. Add a dash of hot sauce if desired. Sprinkle with a little of the remaining cheese.
Fold in the sides of the tortilla, then roll tightly from the bottom up, tucking in the sides as you roll.
If enjoying immediately, you can toast the burritos in a dry skillet for about 1-2 minutes per side until golden and crispy.
If saving for later, let the burritos cool completely, then wrap each one tightly in aluminum foil or parchment paper. Place in a freezer-safe bag and freeze for up to 3 months.