Place whole peppers on hot grill or under broiler and char until blackened all over completely. Remove to brown paper bag;close bag and let stand in sink about 20 minutes. Remove stem and seeds and most of black charred skin. Slice peppers and place in bowl.
Add cheese, basil, onions, anchovy and capers to bowl with peppers and toss to mix lightly.
Make dressing by whisking oil, vinegars, garlic, salt and pepper; taste and season as desired. Pour over vegetable cheese mixture and mix. Let stand at least 20 minutes to blend flavors at room temperature. Serve with bread.
Salad can be refrigerated 24 hours. Bring to room temperature before serving.