Cut bell peppers in half lengthwise; discard seeds and membranes. Place pepper halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil 15 minutes or until blackened. Place in a zip-top plastic bag; seal. Let stand 15 minutes. Peel and cut into 1-inch strips.
Combine bell peppers, anchovy paste, and next 5 ingredients (through garlic) in a medium bowl, stirring until well blended; let stand 30 minutes. Sprinkle with basil and olives.