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1
Preheat the oven's broiler and set the oven rack about 6 inches from the heat source.
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2
Arrange the pepper pieces on the broiler rack so they don't touch each other, and broil until the skin is mostly charred and the peppers are softened, 8 to 10 minutes. Place the peppers into a resealable plastic zipper bag and allow to cool; strip off skin once cooled. Coarsely chop the peppers.
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3
Place the chopped peppers, onions, celery, garlic, chicken stock, and bay leaves into a large saucepan over medium heat, and bring to a boil. Cover, reduce heat to medium-low, and simmer until the onions are and celery are tender, about 15 minutes. Stir in 2 28-ounce cans of diced tomatoes, and remove from heat. Remove and discard bay leaves.
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4
Pour the soup into a blender, filling the pitcher no more than halfway full. Hold down the lid of the blender with a folded kitchen towel, and carefully start the blender, using a few quick pulses to get the soup moving before leaving it on to puree. Puree in batches until smooth. Alternately, you can use a stick blender and puree the soup right in the cooking pot.
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5
Return the blended soup to the saucepan, and stir in the 14.5 ounce can of diced tomatoes and the Parmesan cheese. Bring the soup to a simmer over medium-low heat, whisking constantly to melt the cheese. Season to taste with salt and pepper.
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6
Bring a pot of water to a boil, and stir in the tortellini. Boil the tortellini over medium-low heat until tender, about 5 minutes; drain in a colander set in the sink, rinse with water, and stir into the soup.
