In a small sauce pan, heat olive oil and garlic over a medium heat. Saute until softened, about 1 minute. Add tomato paste, stir to combine. Cook for one minute. Add tomatoes, salt and sugar, whisk until tomato paste is fully incorporated.Simmer for 8-10 minutes until thickened. Set aside.
Heat a large cast-iron skillet or griddle to a medium heat.
Spread about 2 tablespoons of sauce on each slice of bread. Top with four ounces of slices of cheese. Top with 4-5 leaves of basil.
Drizzle with a little bit of olive oil. Season with salt and pepper. Place the other two pieces of bread, sauce side down on cheese and basil. Brush tops with butter. Season with a bit of salt and pepper.
Place sandwich butter-side down in a skillet heat to medium (work in batches if needed), brush other side with butter. Cook until golden brown and crispy on each side and the cheese is melted. (If you are having a hard time getting the cheese to melt, pop into a 350 degree oven for a few minutes.