Heat a 12-inch cast-iron skillet or griddle over medium heat.
Top four slices of bread with 2 tablespoons of sauce, 5 basil leaves, and two slices of cheese (folding or cutting the cheese to fit the bread).
Top the cheese with 1 tablespoon of the sauce. Top with the remaining pieces of bread. Lightly coat the top piece of bread with olive oil cooking spray (or brush with olive oil).
Place sandwich, oil side down in the skillet or griddle (work in batches if needed), spray or brush the other side of the sandwich with olive oil.
Cook, turning once, until golden brown and crispy on each side and the cheese is melted.
Meanwhile, heat the remaining sauce in a small saucepan and serve the heated sauce with the sandwiches for dipping.
