In a large bowl, mix the onions, tomatoes, garlic and basil, taking care not to mash or break up the tomatoes too much. Add the balsamic vinegar and extra virgin olive oil. Add salt and pepper to taste. Mix again. Cover and chill for at least an hour. This will allow the flavours to soak and blend together.
Slice the baguette diagonally into thick slices, brush with olive oil and lightly toast them until they are light brown on both sides. Serve the mixture on the warm slices of bread. If you prefer the mixture at room temperature, remove from the fridge half an hour before serving.