1. The night before cooking, core, halve and seed tomatoes. Thinly slice garlic and combine in a resealable bag with tomatoes. Refrigerate overnight.
2. In the morning, combine tomatoes and garlic with broth and 1/4 cup of the basil leaves in a 4 1/2-quart slow cooker. Season with salt and pepper, cover and cook on HIGH for 6 hours or on LOW for 8 hours.
3. Once soup is almost done, heat panini press. Place 5 slices of the bread on a work surface. Spread 1/2 tsp pesto on each slice. Cut mozzarella and tomatoes into 10 thin slices each. Place 2 slices of the mozzarella on bread. Add 3 basil leaves to each sandwich and top each with 2 slices tomato. Top with 5 remaining bread slices and coat both sides of sandwiches with nonstick cooking spray. Cook sandwiches in panini press for 3 minutes (2 or 3 sandwiches per batch), until browned and cheese is melted.
4. While sandwiches cook, ladle half the tomato mixture into a blender. Blend until smooth. Add remaining tomato mixture to blender if there is space (or do in batches); blend until smooth (or you can use an immersion blender instead). Divide among 5 bowls (about 1 1/3 cups per serving). Serve with a sandwich.