Preheat the barbeque to a medium-high heat.
For the burgers: In a large bowl, mix the beef, onion, parsley, Pecorino, and egg yolk and stir well until all ingredients are evenly distributed.
Divide the mixture in 4 equal portions and shape your burgers.
Grill your burgers 3 to 4 minutes on each side for medium-rare, cook longer for desired degree of doneness, or until an instant read thermometer inserted in the center of the burger reads 165 degrees F for medium. Place the provolone cheese slices on top of the burgers the final minute of grilling.
Move the meat to a large platter to cool off slightly and rest 5 minutes. Meanwhile, lightly toast the burger buns.
Serve your burgers dressed with lettuce, avocado slices, and tomatoes.