Season the chopped chicken with salt and pepper.
Heat remaining olive oil in a large skillet or pan, over medium-high heat.
Once the oil is ready, start browning the chicken. Do this in batches, to leave enough space between the pieces of chicken.
Take the browned chicken out of the pan and set them aside.
Once you have finished with the chicken, adjust heat to medium. Add garlic and onion.
Cook until onion has softened a bit. Add prosciutto and mix.
Add the chicken back into the pan.
Add salt, pepper, peperoncino, tomato paste, and tomatoes. Mix to combine.
Add torn basil leaves and mix.
Adjust the heat back into medium-high and cover the pan with a lid.
Bring to a boil. Adjust the heat to medium-low and simmer for about 25 minutes, or until the chicken is cooked.
Take the pan out of the heat and add the chopped, roasted peppers. Drizzle with the balsamic vinegar and mix to combine.
Serve, and add more fresh basil, if preferred.