Heat the oven to 350 degrees F. Line a rimmed baking sheet with parchment.
Lay out 6 horizontal strips of bacon on the prepared baking sheet. To make a lattice, fold every other strip of bacon in half onto itself and lay one strip of bacon in the middle, vertical to the folded strips. Unfold the strips back over the vertical strip of bacon. Repeat this process using alternating vertical strips to weave into a lattice. (The bacon lattice should have an equal number of horizontal and vertical strips.) Bake until nearly cooked but still very pliable, about 15 minutes. Slide the bacon lattice onto a paper towel-lined plate and allow it to cool, 10 minutes.
Raise the oven temperature to 450 degrees F.
Crack the eggs into a bowl and beat them with a fork. Heat the butter in a small saute pan over medium heat. Add the eggs and scramble until cooked to desired doneness.
Spoon the eggs into the middle of the bacon weave and top with the Cheddar and salsa. Roll the bacon into a burrito, using a toothpick if needed to hold the burrito together.
Put the burrito on the baking sheet and return it to the oven to melt the cheese and fully crisp the bacon, about 10 minutes.