Peperonata: Heat oil in wide pan. Stir-fry peppers for about 5 minutes. Briefly stir-fry onion and garlic. Add wine and water, bring to a boil, simmer over medium heat for about 20 minutes, season.
Chicken: Heat oil and all ingredients up to and including parsley in a wide frying pan. Add the chicken, cover with a lid and simmer for about 10 minutes, season with salt. Arrange the chicken on the peperonata and sprinkle with Sbrinz.