Heat oil in large nonstick skillet over medium-high heat.
Add tomatoes, cut-side-down. Cook until starting to brown. Turn; cook until caramelized.
Combine butter and red pepper flakes. Rub 1 side of each bread slice with cut side of garlic. Spread same side with butter mixture.
Place 4 slices, buttered-side-down, in skillet over medium heat. Top each with 1 slice Mozzarella, tomatoes, Feta, onions, and basil; drizzle with balsamic glaze. Top with another Mozzarella slice and bread slice, buttered-side-up. Grill, turning once until bread is golden brown and cheese is melted. Garnish with basil sprigs, if desired.