Cut the peppers in half, de-seed and brush the skin with olive oil. Put on a baking try skin-side up and grill in the oven until the skin turns dark brown (alternatively barbeque them).
Transfer the peppers to a dish, then cover this with a lid or plate (or clingfilm). Leave to "sweat" for about 10 minutes. When cool, peel the skin off and cut the flesh into long strips.
Mix together the dressing ingredients.
Drain and wipe dry the mozzarella. Depending on how you want to use the salad, slice or tear it into pieces.
Toss the pepper slices, mozzarella bits and the dressing together. Garnish with basil leaves. Serve at room temperature.