Prepare a medium-hot charcoal fire or heat a gas grill for 20 minutes on high. Put the onion, peppers, chile, mushroom, and eggplant slices on the grill. Grill the onion until it can be easily pierced by a skewer (about 45 minutes), the peppers and chile until charred black and the skins are blistering (about 20 minutes), the mushroom until soft and golden brown (about 20 minutes), and the eggplant until branded with grill marks (about 15 minutes).
When the peppers and chile are cool enough to handle, peel them and remove their seeds. Peel the onion. Put the onion, peppers, chile, eggplant, mushroom, chopped tomatoes, and garlic in a food processor. Process until the vegetables are a purée. Pass through a food mill or a strainer and transfer to a saucepan; stir in the olive oil and cream. Turn the heat to medium, bring to a gentle boil, and then simmer until the sauce is dense, smooth, and reduced to about 4 cups, 30 to 40 minutes.
Meanwhile, bring a large pot of well-salted water to a vigorous boil and add the ravioli. Cook until the ravioli are puffy and bobbing on top of the water, pushing them down occasionally (if using frozen ravioli, follow the directions on the package). Test one to be sure it's fully cooked; drain and then cover with the sauce. Serve with freshly grated Parmigiano, if you like.