In a small bowl, whisk together balsamic vinegar, olive oil, minced garlic, and oregano to create the marinade.
Place the flank steak in a shallow dish or resealable bag, pour the marinade over it, and let sit for 30 minutes at room temperature.
Preheat an outdoor grill or indoor cast-iron grill pan to medium-high heat.
Remove steak from marinade and season both sides with salt and pepper.
Grill the steak for 4 to 5 minutes per side or until the internal temperature reaches 135 degrees Fahrenheit for medium-rare.
Transfer steak to a cutting board and allow to rest for 10 minutes to retain juices.
Slice the steak thinly against the grain.
Arrange the steak on a platter and layer alternating slices of fresh mozzarella and tomatoes over the beef.
Garnish with fresh basil leaves and drizzle the balsamic glaze over the entire dish.