Preheat a charcoal grill for medium heat and lightly oil the grate.
Thread beef, artichoke hearts, bell pepper, zucchini, onion, mozzarella, and bread onto skewers, placing cheese and bread close together towards the ends.
Mix vinegar, olive oil, salt, and pepper together in a bowl and drizzle over kabobs.
Grill kabobs, turning frequently, until vegetables are crisp-tender and beef is firm and hot in the center, about 10 minutes.
Sprinkle fresh basil on top of the kabobs.
Placing cheese and bread next to each other on the ends of the kabobs ensures less heat from the grill and that cheese will melt onto the bread.