In a small saucepan over medium heat, add the diced tomato, basil, and olive oil. Cook for about 5 minutes until the tomatoes begin to soften.
While the sauce base is cooking, heat a skillet over medium heat. Butter both sides of each slice of bread.
Place one slice of bread in the skillet. Layer with cheddar and white cheddar cheese, then spread pesto or aioli over the cheese if using. Top with the second slice of bread.
Grill for about 3 to 4 minutes per side, or until both sides are golden and the cheese is fully melted.
Once the tomato mixture has cooked down, pour in the jar of vodka sauce. Stir and cover. Let it heat over medium-high for about 4 to 5 minutes while your sandwich finishes cooking.
Let the grilled cheese cool slightly, then slice and serve with the warm tomato basil dip on the side.