Slice the chicken into thin strips and sprinkle evenly with sea salt and ground pepper.
Heat the butter in a large heavy skillet over medium-high heat, then add the chicken strips in a single layer. Cook until each side is nicely browned, about 8 minutes, using batches if needed. Remove chicken and set aside.
In the same skillet, add the diced onion and garlic. Cook over medium-high heat until the onion turns golden and aromatic, roughly 5 minutes.
Pour in the chicken stock along with the drained roasted red peppers. Allow the liquid to simmer and reduce by half, about 5 minutes, intensifying the flavors.
Turn off the heat completely and gradually whisk in the heavy cream and freshly shredded Parmesan cheese to form a smooth, creamy sauce without lumps.
Reactivate medium-high heat and stir in the Italian seasoning and the drained pepperoncini peppers. Taste and add more salt if needed.
Return the browned chicken pieces to the pan and let them simmer gently until fully cooked to 165°F and the sauce thickens to coat the chicken nicely. If the sauce thickens too much, add extra chicken stock one tablespoon at a time.
Serve immediately over your choice of rice, pasta, or roasted vegetables. Top with additional Parmesan and fresh parsley if you like.
