Preheat oven to 400 degrees F.
Place tomatoes into baking dish along with garlic and onion. Drizzle with olive oil. Season with salt and pepper.
Place into oven and roast for 40-50 minutes, until onions are cooking through and soft.
Remove from oven and let rest for 10 minutes.
Once tomatoes have cooled a bit, transfer roasted tomatoes, onion, garlic, and juices in the pan into a blender. Blend for a minute or two until smooth and creamy. You may need to do this in two separate batches depending on the size of your blender.
To make the grilled cheese: Spread ½ a tbsp of butter on the inside of each bread slices. Add ½ cup of grated cheddar cheese onto 4 bread slices and place the buttered bread on top to sandwich. (Butter on the inside, mayonnaise will go on the outside).
Place a skillet over medium heat.
Spread ½ tbsp of mayonnaise on top of the bread (on the outside portion). Flip it into a heated skillet so that the bread slice with the mayonnaise gets toasted first. Spread ½ tbsp of mayonnaise onto the other slice.
Toast on each side for about 2-3 minutes, until cheese is melted and bread is golden.
Repeat with remaining grilled cheese sandwiches.
Carefully remove the lid from the blender and pour into serving bowls. Drizzle with additional olive oil, a splash of cream, and garnish with basil. Serve with grilled cheese sandwiches.