Heat oil in a large 12-inch skillet over medium-high heat until simmering.
Cook hash browns until golden brown, then remove them from the pan onto a paper towel-lined plate.
Add sausage, onion, and peppers to the skillet and cook until no pink remains. Drain off the grease.
Add the hash browns back to the pan.
Pour the lightly beaten eggs into the skillet and cook until they are set, stirring frequently.
Pour in can of green chile sauce and stir to combine.
Add salt and pepper to taste.
Remove the burrito filling from the heat.
Spoon roughly 1/2 cup filling onto the bottom ⅓ of each tortilla.
Sprinkle with 2 T. cheese.
Fold the sides and then the ends over and roll up the burrito as tightly as possible.
Heat a clean skillet and place burritos, a few at a time, in the warm skillet seam side down.
Cook each burrito on all sides until the tortilla is golden brown and crispy.
Cut twelve large pieces of foil (about 18 inches) and twelve slightly smaller pieces of parchment paper (about 16 inches). Place one piece of parchment paper on top of each piece of foil.
Allow burritos to cool slightly, then place them on your prepared foil.
Wrap tightly, label, and freeze up to 2 months.