1. Heat grill (or grill pan) to medium. Brush squash and bread with 1 tablespoon olive oil; season with half of the salt and pepper. Add squash and bread to grill; cook, turning occasionally, until squash is tender and bread is charred (4-6 minutes). Rub bread with cut side of garlic clove.
2. In a large bowl, combine remaining 2 tablespoons olive oil, remaining salt and pepper, and vinegar; whisk well. Cut squash and tear bread into 1-inch pieces; toss in dressing with arugula and olives. Divide salad among 6 plates, and top each with 4 pieces of burrata. Drizzle with additional olive oil and sprinkle with sea salt, if desired.
Note: The sum of constituent fats (saturated, monounsaturated, polyunsaturated) may not always equal the total-fat value.