In a large pot, heat olive oil over medium-high heat. Add garlic. Stir and cook for 30 seconds. Add onion. Stir and cook until translucent. About 6 or so minutes.
Add diced tomatoes (undrained), chicken broth, and sugar. Stir and bring to a low simmer. Cook for 15 minutes or until soup thickens.
Stir in heavy cream, basil, and oregano. Season with salt and pepper.
Using an immersion blender (or carefully transfer soup to a blender. If you use a blender be very careful handling this very hot soup), puree soup until there are no large chunks left.
Serve soup in bowls with the grilled Mozzarella cheese sandwiches. Enjoy!