In a small bowl, whisk together the balsamic vinegar, olive oil, Dijon mustard, honey, garlic, salt, and pepper.
Place the flank steak in a shallow dish or resealable bag and pour in half the marinade. Refrigerate and marinate overnight (or at least 12 hours).
Preheat grill to medium-high heat. Remove the steak from marinade and shake off excess.
Grill steak 3–5 minutes per side or until desired doneness. Let rest for 5 minutes before slicing.
Meanwhile, grill the cherry tomatoes until lightly charred, about 3–5 minutes. Alternatively, blister in a hot skillet.
Slice steak thinly against the grain. Arrange on a platter and top with blistered tomatoes, mozzarella chunks, and sliced basil.
Drizzle with remaining marinade and serve immediately.
