Season chicken with salt and pepper
Grill Instructions: If you're using an outdoor grill: pre-heat the grill for at least 10 minutes. Cook chicken on grill grates for 4 to 5 minutes per side for thighs and 5 to 6 minutes per side for chicken breasts. If you have very large chicken breasts you might want to grill them for 7 minutes.
Skillet/grill pan instructions: If you're using an indoor grill pan or skillet, pre-heat for 5 minutes over medium-high heat. cook on a pre-heated pan for 4 to 5 minutes per side for thighs and at least 5 to 6 minutes per side for chicken breasts.
If you have a probe thermometer you should be looking for 165 degrees F (73 C) for all of your chicken pieces. You should be able to pull the chicken off the grill or out of the pan at 5 degrees less than your target temperature and it will carry over cook those 5 extra degrees.
Let chicken rest 5 minutes after cooking and before slicing.
If you have a broiler, turn it on when the 5 minutes of chicken rest time have ended. Otherwise, turn your oven to 350 degrees F (165 C). The broiler or oven is to warm the sandwich through and potentially melt the mozzarella.
If each chicken piece is oddly sized or too small for your rolls, slice the chicken to fit the sandwich rolls.
Toast your rolls if desired.
Add a generous amount of pesto to the bottom roll. Add a few roasted red pepper pieces on top of the pesto sauce.
Top the pesto and peppers with chicken and then lay a couple of slices of mozzarella on top of the chicken.
Add each bottom bun, topped with pesto, peppers, chicken, and mozzarella to a sheet pan and place under the broiler or into the oven. If you are broiling, pay very close attention and broil for 2 to 3 minutes. The broiler could burn everything really quickly so be careful. If you are using your oven set to 350 F/165 C, leave the mozzarella-topped chicken sandwich bottoms in the oven for 5 to 7 minutes or until the mozzarella becomes soft and melty.
Remove sandwich bottoms from the oven when the mozzarella starts to look like it's melting.
Add more pesto to the inside of the top roll if you want. Then add the roll tops to enclose the sandwiches.
Serve sandwiches and enjoy.