Char peppers directly over gas flame or under broiler until blackened on all sides. Enclose in paper bag; let stand 10 minutes. Peel, seed, and slice peppers thinly. Combine basil leaves, garlic, and salt in processor and blend to coarse puree. With machine running, gradually blend in oil. Transfer basil oil to small bowl. (Peppers and basil oil can be made 1 day ahead. Cover separately and chill.) Arrange prosciutto around edge of platter. Arrange cheese slices within circle of prosciutto and tomatoes within circle of cheese. Tuck in egg slices; top with pepper strips. Sprinkle salad with olives; drizzle with some basil oil. Serve with remaining basil oil.