In a shallow dish, combine 2 tablespoons olive oil, minced garlic, oregano, 1 teaspoon kosher salt, 1/2 teaspoon black pepper, and 1 tablespoon balsamic vinegar. Add the flank steak, turning to coat thoroughly. Let marinate at room temperature for 15-30 minutes while you prepare the other components.
In a small saucepan, combine 1/2 cup balsamic vinegar, honey, minced garlic, and black pepper. Bring to a simmer over medium heat, then reduce heat to low and cook for 8-10 minutes, stirring occasionally, until reduced by half and slightly thickened. It should coat the back of a spoon. Remove from heat and let cool slightly; it will thicken more as it cools.
In a medium bowl, combine halved cherry tomatoes, mozzarella balls, and torn basil leaves. Drizzle with 2 tablespoons olive oil and a pinch of flaky sea salt. Toss gently to combine. Set aside.
Preheat grill to high heat (about 450-500°F). Brush the grates with oil. Remove steak from marinade, letting excess drip off. 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.
After resting, slice the steak thinly against the grain at a slight angle. Arrange the Caprese salad on a large white platter or individual plates. Fan the sliced steak over the salad. Drizzle generously with the balsamic dressing. Garnish with additional whole basil leaves.