In a food processor or blender, combine the garlic, basil, egg yolks, salt, pepper, and Dijon mustard and process to combine. With the machine running, add the oil in a slow, steady stream until it is all added and the mixture is emulsified. Add the lemon juice and check the seasoning.
Combine the ginger, garlic, green onions, chile flakes, and peanut oil. Add the chicken and toss to coat. Marinate overnight in the refrigerator.
Preheat the oven to 350 degrees F.
Remove the chicken from the marinade and place in a small roasting pan or on a baking sheet. Roast the chicken for 15 to 20 minutes, or until cooked through. Cut the chicken crosswise into very thin slices.
Raise the oven temperature to 450 degrees F.
Slice the rolls horizontally and place on a baking sheet with the top half cut-side down and the bottom half with cut-side up. Place 1 slice of provolone on the bottom half of each roll. Cook until the cheese is melted and the rolls are lightly toasted, about 3 minutes.
Place 1/4 of the chicken on top of the melted cheese. Top with romaine lettuce, tomato, and red onions. Spread some of the aioli on the top half of the roll and place the roll on top of the sandwich.