Preheat oven to 375° F. (If baking and eating burritos right away. If freezing burritos, no oven is needed until you are ready to warm and eat them.)
Heat the olive oil in a medium/large nonstick skillet over medium heat. Once hot, add the vegetables and cook, stirring often, until softened, about 4 minutes. Transfer vegetables to a clean medium size bowl.
Add the sausage to the pan and cook, crumbling, until it is browned and fully cooked. Transfer sausage to the bowl with the vegetables, leaving any grease behind.
Crack the eggs into a medium mixing bowl and add the salt. Whisk vigorously, until eggs are completely combined and uniform.
Wipe out the skillet and add the butter. Heat over medium heat until the butter is melted, using a rubber spatula to spread it around the pan. Pour the eggs into the pan and reduce the heat to medium low. Let the eggs cook without stirring for 30 seconds, then use a rubber spatula to gently and slowly scrape across the bottom and around the edges of the pan as the eggs cook, scraping across different areas of the pan and in different directions so that no bits of egg dry out. As the eggs cook, also fold them gently to help them cook evenly.
Once the eggs are cooked, turn off the heat and add them to the bowl with the sausage and veggies. Stir gently to mix everything together.
To assemble the burritos, place 1/8 of the egg/sausage/veggie mixture on top of each tortilla, placing it down the tortilla in a line slightly off center (for easier wrapping). Sprinkle 1/4 cup of shredded cheese on top of the egg mixture. Tightly wrap up each tortilla, burrito-style.
Burritos can be eaten as is, baked to melt the cheese and crisp the tortillas, or frozen for later.
Optional: To bake to crisp tortillas (right before serving): Place burritos seam side down on a parchment paper-lined baking sheet and bake in a 375° F oven for 5-10 minutes, until warmed through and lightly browned. Then serve.
To freeze: First flash freeze burritos by placing on a baking sheet in the freezer for 2 hours. Once frozen, transfer to a zip-top plastic bag and store in the freezer for up to 1 month.
To thaw and heat a frozen burrito: Thaw overnight in the refrigerator. To reheat, microwave on high power for 30-45 seconds to start heating up the center of the burrito. Then heat in a 350° F oven for 10 minutes, or until fully hot in the center. Thawed burritos can also be fully heated in the microwave. Using the oven gives you a crispier tortilla, and the microwave a chewier tortilla.