Why not grill the chicken and bread for this sandwich instead of broil them? Laura Ortega, who lives and cooks in the land of air conditioning— in Palm Desert, California— told us that it’s far easier (and cooler) for a quick lunch to turn on the broiler than fire up the grill. Suit yourself! Either broiled or grilled, these ingredients make for a delicious sandwich.
Quick-roast and peel bell pepper and cut into 1-inch-wide strips. With a vegetable peeler shave enough Parmigiano-Reggiano to measure about 1/2 cup.
Put chicken between 2 sheets of dampened plastic wrap and with a rolling pin or flat side of a meat pounder lightly pound to about 1/4 inch thick. Arrange chicken on lightly oiled rack of a broiler pan.
In a small bowl whisk together vinegar, 1 tablespoon oil, pepper, and salt to taste. Brush chicken with vinaigrette and broil 2 to 3 inches from heat 5 minutes. Turn chicken over and brush with vinaigrette. Discard any remaining vinaigrette and broil chicken until just cooked through, about 5 minutes more. Transfer chicken to a plate and keep warm, loosely covered with foil.
Cut four 1/2-inch-thick slices from middle of loaf and lightly brush both sides of each slice with remaining 3 tablespoons oil. Toast bread slices on broiler pan under broiler. Halve garlic clove crosswise and rub over 1 side of each slice of toast.
Assemble sandwiches with chicken, peppers, cheese shavings, and basil and season with salt and freshly ground pepper.