Season the sliced boneless chicken breast or thighs with sea salt and ground black pepper. Melt the unsalted butter in a large, heavy pan over medium-high heat. Add the seasoned chicken to the pan and brown on all sides, turning every couple of minutes, for about 8 minutes. The chicken doesn't need to be fully cooked at this stage—just nicely browned for flavor. Once browned, remove the chicken from the pan and set it aside.
In the same pan, add the diced white onion and minced garlic. Sauté over medium heat until the onions are browned and fragrant, about 5 minutes. Next, add the chicken broth and sliced roasted red peppers. Stir and let the mixture simmer, reducing the liquid by half for about 5 minutes. Deglazing the pan at this stage helps lift all those delicious browned bits left from searing the chicken.
With the heat turned off, gradually stir in the heavy cream and grated parmesan cheese, whisking vigorously to create a smooth, creamy sauce. Turning off the heat while adding these ingredients helps prevent the cream from curdling. I find that a slow hand with the cream and constant whisking really ensures a silky texture.
Turn the heat back up to medium-high. Add the Italian herb seasoning and drained pepperoncini peppers—feel free to use sliced or whole peppers based on your preference. Return the browned chicken (from Step 1) to the pan. Stir everything together and let the sauce reduce by half while finishing cooking the chicken to an internal temperature of 165°F. If the sauce thickens too quickly, add a splash more chicken broth to loosen it up. I like to keep a little extra broth on hand just for that reason.
Remove the pan from heat. Garnish the finished creamy pepperoncini chicken with chopped fresh parsley for a burst of color and freshness. Serve the dish hot, either on its own or over pasta, rice, or your favorite vegetables.