To make the caprese mixture, place the chopped tomatoes, Mozzarella cheese and basil into a medium-sized bowl. Add the olive oil and oregano. Season with sea salt and toss to combine. Set aside.
Meanwhile, heat a barbecue grill or chargrill pan on medium-high heat. Brush both sides of the bread with olive oil. Cook the bread for 2 minutes on each side or until charred.
Rub the cut side of the garlic halves over 1 side of each slice of bread. Spoon the caprese mixture over the chargrilled bread. Serve immediately.