1. Preheat oven to 400°.
2. Combine 1 teaspoon oil, tomatoes, and garlic on a baking sheet. Bake at 400° for 20 minutes. Remove skins from tomatoes; discard skins. Squeeze garlic to extract pulp; discard garlic skins. Combine tomatoes, garlic pulp, basil, salt, and pepper in a mini food processor; pulse 10 times.
3. Combine mayonnaise and cream cheese in a medium bowl. Add cheddar, stirring well to combine (mixture will be very thick). Spread one-fourth of cheese mixture (about 2 tablespoons) over each of 4 bread slices; top each with about 1 1/2 tablespoons tomato mixture and 1 bread slice. Lightly coat outsides of sandwiches with cooking spray.
4. Heat a large skillet over medium heat. Add 1 teaspoon oil; swirl to coat. Place sandwiches in pan; cook 3 minutes or until lightly browned (do not flip). Remove sandwiches from pan. Add remaining 1 teaspoon oil; swirl to coat. Turn sandwiches over, and add to pan; cook 3 minutes or until lightly browned and cheese melts. Cut in half; serve immediately.