Bring a pot of water to a boil (large enough to submerge your head of cabbage).
Once boiling, add cored cabbage (1 head) and blanch for about 3 minutes, then use 2 tongs to remove each of the leaves. If they're difficult to remove, allow the leaves to blanch longer. Set blanched leaves aside on a plate as you cook remaining leaves. You'll need 8 leaves in total, so feel free to discard the center smaller leaves.
Optional: Once leaves are cool enough to handle, use a small knife to remove some of the core's thickness by dragging the blade over the top of the core.
Meanwhile, cook the bacon (8 slices) in a large skillet over medium-low heat.
Set cooked bacon aside on a paper towel-lined plate and remove all but 1 tablespoon of bacon grease from the pan.
Add whisked eggs (8), salt (1/2 teaspoon) and pepper (1/4 teaspoon) and scramble the eggs as they cook.
Lay two cabbage leaves on a flat surface, with the center of the leaves slightly overlapping (see photos above).
Start with a layer of cheddar, followed by eggs, bacon, salsa, avocado, and last a layer of cheddar again (the cheese will act as the "glue" to hold our burritos together).
Fold the left and right edges of the cabbage leaves over the filling, then roll the leaves away from you to form a burrito.
Option to bake burritos in the oven to melt the cheese at 400 F for 10 minutes.
Slice in half, serve warm, and enjoy!