Preheat oven to broil on low.
On a baking sheet, toss together the tomatoes, red onion, jalapeños, garlic, olive oil and salt and pepper to taste. Broil, stirring every 10 minutes, until all the vegetables are charred (not burnt), about 30 minutes. Remove vegetables, increase broiler to high.
Transfer charred vegetables to a large Dutch oven. Add tomato purée and vegetable stock. Bring the mixture to a boil, reduce to simmer and cook for 30 minutes.
For the crostini, arrange baguette slices on baking sheet, broil,, turning once until lightly toasted, about 2 minutes. Rub each slice with garlic clove. Top each with some of the mozzarella and Cheddar cheeses. Broil until cheese is bubbly and golden, 1 to 2 minutes.
Purée the soup mixture and serve with as many crostini as you can stack.