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Prep your tomatoes and onion. Place on a shallow baking sheet with the baby carrots in one layer. Drizzle with about a quarter cup of extra virgin olive oil and slow roast the vegetables in the center of your oven at 250 degrees for three hours. Keep an eye on the roasting vegetables, give them a turn every half hour so they roast evenly. If any of the vegetables appear to be roasting too quickly, move them around. With about an hour of roasting left, add the garlic cloves.
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After three hours, remove the roasted vegetables and place them into a food processor or blender. They are going to be hot, so gently pulse them at first and if necessary allow any steam generated to get out of the blender or processor. Continue to puree the vegetables until they are as smooth as possible.
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Put the pureed vegetables into a large sauce pan over medium heat. Add the Parmigiano-Reggiano rind, broth, chopped basil leaves, oregano, and red pepper, and give it all a good stir.
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Bring to a simmer and keep simmering while stirring occasionally for about 20 minutes. Add a pinch of salt and pepper to taste.
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After about 20 minutes of simmering, you have a decision to make. Do you filter the soup or not? I like to filter the soup so it becomes a more silky smooth tomato soup. However, my wife likes the soup without it being filtered. Either way is fine I suppose, it really comes down to preference. If you decide to filter, run the soup through a fine mesh collander or food mill, and collect the liquid in a bowl underneath. When finished, put the liquid back into the sauce pan and bring back to a simmer. Check the salt and pepper seasonings one more time.
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When finished, serve with some fresh chopped basil leaves, grated Parmigiano-Reggiano and some slices of crisp Italian bread. And enjoy!