Preheat the grill for high heat. Place the red and yellow peppers on a grill pan, cut side down.
Grill the peppers until the skin is charred, about 5 minutes. Place the peppers in a paper bag and set aside until cool enough to handle.
Preheat the oven to 200 C / Gas 6. Place the slices of bread on a baking tray and brush them lightly with 1 tablespoon of the olive oil.
Bake the bread until crisp and golden, about 12 minutes.
Meanwhile, peel the skin off the peppers and coarsely chop them. Mix the peppers with the basil leaves in a bowl. Drizzle the balsamic vinegar and the remaining olive oil over the peppers and season with salt and pepper.
Divide the peppers and their dressing among the bread slices and serve immediately.