Pat the flank steak dry with paper towels. In a small bowl, whisk together 2 tablespoons olive oil, minced garlic, oregano, salt, and pepper. Rub the mixture all over the steak. Let it marinate at room temperature for 15 minutes while you prepare the grill and other components.
In a small saucepan, combine balsamic vinegar, honey, and minced garlic. Bring to a simmer over medium heat, then reduce heat to low and cook for 5-7 minutes, until slightly thickened and reduced by about one-third. Remove from heat and whisk in Dijon mustard and 1/4 cup olive oil until emulsified. Set aside to cool.
Preheat your grill to high heat (about 450-500°F). Brush the grill grates clean and oil them lightly. Place the flank steak on the hottest part of the grill. Grill for 5-7 minutes per side for medium-rare (130-135°F internal temperature), or until desired doneness. Transfer to a cutting board, tent loosely with foil, and let rest for 10 minutes.
While the steak rests, in a medium bowl, gently combine the halved cherry tomatoes, mozzarella balls, torn basil leaves, and 2 tablespoons of olive oil. Season with a pinch of flaky sea salt and a twist of black pepper.
Slice the rested flank steak thinly against the grain (at a sharp diagonal) into 1/4-inch thick slices. Arrange the slices on a white oval platter. Spoon the Caprese salad over and around the steak. Drizzle generously with the balsamic dressing. Garnish with additional whole basil leaves. Serve immediately.