Pat the chicken breasts dry with paper towels. Season both sides generously with salt, pepper, and smoked paprika. Let them sit at room temperature for ten minutes while you prepare the other ingredients.

In a large heavy skillet, heat the olive oil over medium high heat until it shimmers. Carefully place the chicken breasts in the pan. Cook without moving for 4 to 5 minutes, until the underside is golden brown and releases easily. Flip and cook for another 4 to 5 minutes. The chicken should be cooked through (internal temperature of 165 degrees F). Transfer to a plate and tent with foil. Do not wipe the pan clean.

Reduce the heat to medium. Add the butter to the pan and let it melt. Add the diced onion and cook, stirring occasionally, for 3 to 4 minutes until softened and translucent. Add the minced garlic and cook for another 30 seconds, until fragrant.

Stir in the chopped banana peppers and the reserved pickling liquid. Cook for 1 to 2 minutes, letting the peppers release their tangy aroma.

Sprinkle the flour over the pepper mixture and stir constantly for 1 minute. Slowly pour in the chicken broth while whisking to prevent lumps. Then add the heavy cream, whisking until smooth. Let the sauce come to a gentle simmer. It will thicken slightly.

Stir in the dried thyme, oregano, and a pinch of black pepper. If using Parmesan, sprinkle it in and stir until melted. Taste the sauce. It should be creamy, tangy, and savory. Adjust salt if needed.

Place the seared chicken breasts back into the skillet, nestling them into the sauce. Spoon some of the sauce over the top. Reduce the heat to low and let everything simmer together for 5 minutes.

Sprinkle fresh parsley over the top. Serve immediately, or let it rest for a few minutes. The sauce will continue to thicken as it cools.