Place the baked beans in a small saucepan over medium heat. Warm them until heated through, stirring occasionally so they do not stick. Keep the beans warm while you prepare the eggs.
Crack the eggs into a medium bowl and beat them until the yolks and whites are well combined. Season with freshly ground black pepper and any salt needed for your taste.
Melt the butter or margarine in a 10-inch nonstick skillet over medium heat. I prefer a nonstick pan here because it makes the soft scrambled eggs easier to stir and prevents a sticky layer from forming.
Pour the beaten eggs into the skillet and let them begin to set. Add the crumbled bacon, if using, along with the chopped green onions, then stir occasionally until the eggs are cooked.
Warm all six flour tortillas just before assembling the burritos. I recommend keeping them covered after warming because soft tortillas fold more easily and are less likely to crack.
Divide the cooked egg mixture evenly among the six tortillas. Spoon the eggs toward the center rather than spreading them all the way to the edges, leaving room for the beans and cheese.
Top each tortilla with about ¼ cup of warm beans. Add approximately 1 tablespoon plus 1 teaspoon of shredded cheddar cheese to each burrito so the cheese melts into the warm filling.
Fold the ends of each tortilla inward over the filling. Then roll the tortilla tightly from one side to the other, keeping the filling enclosed as you go.
Place the finished burritos seam-side down and serve while they are warm. I like adding salsa just before serving for a fresh, tangy contrast to the smoky beans, eggs, and cheese.