In a food processor, combine butter, mayo and parmesan. Using an S blade, blend until smooth.
Split ciabatta rolls in half and place cut sides down on a plate or clean surface. Spread butter mixture on the outside pieces of ciabatta (both top and bottom pieces).
Heat large skillet over medium-low. Add bottom pieces of ciabatta buns, butter side down, add 2 slices of mozzarella to each bun, top with the top piece of ciabatta. Cook until golden and the bread is crusty.
Carefully flip using a spatula. Squish the ciabatta down using a spatula so the whole domed top of the sandwich cooks and crisps up. Cook for another 5 minutes or so, or until browned and crispy. Remove sandwiches from the pan and slice diagonally into triangles for serving. Place two traingles on each plate.
For the Soup:
Heat olive oil in medium saucepan over medium heat. Add onion with salt and pepper; cook until cooked and transluscent, about 3 minutes. Add garlic and stir, cooking until fragrant, about 30 seconds.
Add in tomatoes, broth and sugar. Stir to combine well. Bring to a simmer. Simmer for about 4 minutes, or until soup is hot. Remove soup from heat. Add in basil and stir. Cover Serve immediately.
To serve: Divide up soup into 4 small soup bowls. Garnish each with a bit of chiffonaded basil and a drizzle of chili oil.
Notes
Work in batches if you don't have a large skillet, or use two skillets at once.Click here to purchase chili oil.Click here for instruction on how to chiffonade basil.