Heat a cast-iron grill pan or traditional grill until very hot.
Toss challah with olive oil and place on grill pan, cook until all sides are grilled or slightly charred, set aside.
In a large bowl, combine tomatoes and mozzarella and set aside.
Immediately before serving, heat a small saucepan over medium heat and reduce balsamic vinegar until thick.
Add grilled challah to tomato mixture and drizzle with reduced balsamic vinegar, olive oil and top with kosher salt to taste.
Serve immediately.