Remove the skin from the sausage and mix the meat with the ground beef.
Form 8 patties.
Refrigerate until ready to grill.

In a medium saucepan, add the olive oil, bell peppers, onion, fennel seeds, salt, and pepper.
Cook over medium-low heat until the vegetables are tender and start to caramelize, about 15-20 minutes.

Remove from heat and add the balsamic vinegar.

Preheat the barbecue.
Cook the burgers for about 3-5 minutes per side or until they are well cooked.

Remove from the grill and place a burger on each thintini bun, also topping with pepper, the onion and bell pepper mixture, and pieces of bocconcini.
Return to the grill, if desired, to warm the bread and melt the cheese.