Combine olive oil, parsley, basil, red wine vinegar, garlic, lime juice, and salt and pepper to taste in a bowl. Mix. If you can, let it sit an hour or two to let the flavors develop. If you are impatient, it is still good!
To build a Caprese sandwich, start by liberally spreading the chimichuri on the bottom half of the bread. Add two big slices of tomato, then two big slices of buffalo mozzarella.
Finish it off with two big basil leaves and a dash of salt and pepper. Put the top on and... delicious! You will probably have enough tomato left over for at least a couple more sandwiches.
Notes
Make the sauce ahead of time so the flavors are well incorporated, but assemble the sandwiches just before serving.