Pat the chicken dry with paper towels. Season both sides with 1 teaspoon kosher salt, black pepper, and Italian seasoning.
Heat olive oil in a large skillet over medium heat. Add the chicken in a single layer, working in batches if needed. Cook for 5 to 7 minutes, flipping halfway through, until golden brown and cooked through to an internal temperature of 165°F. Transfer the chicken to a plate and set aside.
In the same skillet, add the sliced bell pepper, onion, and remaining ½ teaspoon kosher salt. Cook for 2 to 3 minutes, until the vegetables begin to soften.
Add the garlic and cook for 1 minute, stirring often. Be careful not to burn the garlic.
Pour in the chicken broth, scraping up any browned bits from the bottom of the skillet. Simmer for 1 to 2 minutes to reduce slightly.
Stir in the heavy cream, Parmesan cheese, pepperoncini peppers, pepperoncini brine, and red pepper flakes (if using). Bring the sauce to a gentle simmer (do not boil). Cook for 3 to 4 minutes, until slightly thickened.
Return the chicken and any juices to the skillet. Spoon the sauce over the top and simmer gently for another 2 to 3 minutes, until everything is warmed through and coated in the creamy sauce.
Garnish with additional Parmesan and fresh parsley. Serve warm over rice, pasta, mashed potatoes, or cauliflower rice.