Mix first 4 ingredients in bowl. Season with salt and pepper. Arrange 4 bread slices on work surface. Divide half of cheese equally among bread slices. Top with ham, then onion, tomato and remaining cheese. Top sandwiches with remaining bread. Spread herb butter on outside of sandwich tops and bottoms.
Heat large nonstick skillet over medium heat. Add sandwiches and cook until bottoms are golden, about 3 minutes. Turn sandwiches over, cover skillet and cook until cheese melts and bread is golden, about 3 minutes.
