Place one oven rack in the second from bottom position and place another rack in the second from top position. Pre heat the oven to 425℉.
In a large dutch oven empty the whole peeled tomatoes, then using your hands, gently crush the tomatoes. Add the sliced tomatoes, garlic, and 2 tablespoons of the butter. Place 4 basil leaves on top (you can also substitute 4 thyme sprigs instead of the basil). Drizzle with 2 tablespoons olive oil and season with 1 teaspoon salt, and ½ teaspoon black pepper. Add hot sauce, if using.
Roast on the lower rack until the garlic is soft and the mixture is bubbly and thickened, about 45 minutes.
While the soup is roasting, tear or cut the sourdough into 1-inch cubes. Melt the remaining 2 tablespoons butter, adding to a large bowl. Add the Italian seasoning to the butter, then add the sourdough cubes. Toss with a large spoon or your hands to coat the bread with the butter mixture. Spread the bread on a parchment lined baking sheet and place the sheet on the top oven rack to bake during the last 13-15 minutes of roasting the soup. Watch the croutons and remove when they're golden on the edges. The bread will crisp a bit more during the second time in the oven. Remove the bread from the oven and set aside.
Remove the soup and place the pot over medium heat. If you added thyme sprigs in place of basil, remove the sprigs from the pot. Add the vegetable broth to the soup and simmer, stirring to remove the fond from the sides of the oven (Dark brown bits that accumulated in the oven).
Stir in the balsamic vinegar. Using an immersion blender, puree the soup directly in the pot, until smooth. Taste and add more salt and pepper if needed.
Move an oven rack to the middle position in the oven and heat the oven to High on Broil. Sprinkle half of the cheddar cheese over the soup, all of the mozzarella, and half of the Parmesan cheese. Top with the croutons, arranging them in a single layer to cover the soup. Sprinkle the remaining cheddar and Parmesan cheese over the croutons. Broil on the middle rack until the cheese has melted, watching it so not to burn, only 1 or 2 minutes.
Serve immediately, adding more basil or thyme as a garnish. See notes for make ahead instructions.