There are several ways to grill peppers. OVEN - Preheat broiler. Lightly coat the red pepper with olive oil. Grill peppers under the broiler until the skin turns black and the pepper softens slightly. Place pepper into a paper bag to cool for approximately 20 minutes, and then peel off the blackened skin. GAS GRILL - Turn your flame on high, and with metal tongs, place the pepper on the gas burner. Flip over once one side is blackened, continue to do so until the entire pepper has been blackened. Place pepper into a paper bag to cool for approximately 20 minutes, and then peel off the blackened skin.
Season chicken breast with salt and pepper, and place in a skillet over medium-low heat with 1 tablespoon of cooking oil. Cook chicken breast for about 4 minutes on one side, flip over, and cook chicken breast on the other side. Slice chicken breast into small slices.
Preheat oven to 350°F Peel garlic clove, cut in half, and rub cut garlic clove over the flat bread. Place cooked sliced chicken breast onto flatbread, coat the bread with Alfredo sauce, top with half of the grilled red peppers, and sprinkle over mozzarella cheese on top of everything.
Place into the oven and heat until the mozzarella cheese melts (6 to 8 minutes). Remove from oven and top with remaining grilled red peppers and chopped basil. Slice into smaller pieces.