Heat the oven to 375 °F if you plan to bake and serve the burritos right away; otherwise, leave it off for now. The oven is only needed for the final warming and browning stage.

Warm the olive oil in a medium or large nonstick skillet over medium heat, then cook the chopped vegetables for about 4 minutes, stirring often. Move them to a clean medium bowl once they are softened and their raw edge has faded.

Add the sausage to the same skillet and break it into small pieces as it cooks until browned and fully cooked. Transfer the sausage to the bowl with the vegetables, leaving the rendered grease in the skillet.

Crack the eggs into a medium mixing bowl, add the salt, and whisk until the yolks and whites become completely uniform. The mixture should look smooth and evenly colored with no clear streaks remaining.

Wipe out the skillet, melt the butter over medium heat, then add the eggs and lower the heat to medium-low after 30 seconds. Use a rubber spatula to slowly scrape and fold from different directions until tender curds form without dry patches.

Turn off the heat and gently fold the eggs into the bowl of sausage and vegetables. The egg curds should still look moist and soft rather than crumbly or firm.

Place one-eighth of the filling in a line slightly off-center on each tortilla, then scatter 1/4 cup of cheese over the filling. Fold both sides inward, pull the bottom flap firmly over the filling, and roll forward until the seam lands underneath.

Serve the wrapped burritos as they are, bake them for a crisp finish, or prepare them for later heating. A properly rolled burrito feels compact and holds its shape when gently lifted.

For a crisp baked finish, arrange the burritos seam-side down on a parchment-lined baking sheet and bake at 375 °F for 5 to 10 minutes. They are ready when the tortillas are lightly browned and the cheese has melted through the center.

For later use, place the burritos on a baking sheet and freeze for 2 hours before moving them to a zip-top plastic bag. Freezing them separately first keeps the wrapped burritos from sticking together.

Thaw a frozen burrito overnight in the refrigerator, microwave it on high for 30 to 45 seconds, then heat it in a 350 °F oven for 10 minutes. The oven gives the tortilla a crisper finish, while microwave heating leaves it softer and chewier.