Spread 1 side of each bread slice with butter, and place butter-side-down on a flat surface. Spread pesto on 1 bread slice. Top with shredded Gouda and tomato slices. Place remaining bread slice over to form sandwich, butter-side-up, pushing down gently.
Place on hot grill. Cook until bottom side is golden brown and cheese is slightly melted. Flip sandwich; grill until bottom bread slice browns and cheese has completely melted. Serve immediately.