Spread 1 tablespoon Basil Pesto on 1 side of each slice of bread. Top 4 slices of bread with Marinated Chicken Breast. Top the chicken with the roasted peppers. Place the remaining bread slices, pesto-side down, on top of the peppers.
Combine the basil, garlic and pine nuts in a food processor and pulse until coarsely chopped. Add the 1/2 cup of the oil and process until fully incorporated and smooth. Season with salt and pepper. If freezing, transfer to an air-tight container and drizzle remaining oil over the top. Freeze for up to 3 months. Thaw and stir in cheese.
Marinated Chicken Breasts:
Put the vinegar, herbs, mustard, powder if using and oil in a large resealable plastic bag. Close the bag and shake to combine all the ingredients. Open the bag and drop in the chicken breasts. Close and shake the bag to coat evenly. Freeze for up to 2 weeks.
Thaw in the refrigerator overnight, under cold, running water, or in the microwave at 30 percent power for 1 minute at a time.
Heat a grill or grill pan. When the grill is hot, place the chicken on the grill and cook for about 4 minutes per side, or until cooked through. You can also bake the thawed chicken in a 375 degree F oven for 15 minutes, or until cooked through.
If using immediately, add all the oil and pulse until smooth. Transfer the pesto to a large serving bowl and mix in the cheese.