Preheat the grill and set the oven rack about 15cm from the heat source.
Arrange the capsicum pieces on the rack so they don't touch each other, and grill until the skin is mostly charred and the capsicums are softened, 8 to 10 minutes. Place the capsicums into a resealable plastic zipper bag and allow to cool; strip off skin once cooled. Coarsely chop the capsicums.
Place the chopped capsicums, 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 800g tins of diced tomatoes and remove from heat. Remove and discard bay leaves.
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.
Return the blended soup to the saucepan and stir in the 400g tin 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.
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.