Prepare the chicken breasts: Starting from the thickest end, slice each chicken breast in half horizontally to end up with a total of 8 cutlets. Season both sides of the chicken with salt and pepper, to taste.

Spread the flour in a shallow dish. Working with 1 cutlet at a time, dredge the chicken in flour, shaking gently to remove the excess and transfer to a plate.

Heat a large skillet over medium-high heat. Add 2 tablespoons butter and 1 tablespoon oil, and let the butter melt. Once the foam has subsided, add the first 4 cutlets to the pan, and cook until golden brown, 4 to 5 minutes per side. Transfer to a clean plate and repeat the process with 2 tablespoons butter, 1 tablespoon oil, and the remaining 4 cutlets. (Do not wipe out the pan between batches unless flour is burning). Reduce the heat to medium-low.

In the same skillet, melt the remaining 2 tablespoons butter. Add the onion, and cook until it is translucent, about 2 minutes. Add the garlic, red pepper flakes, and tomato paste to the pan. Stir and cook for until the garlic is fragrant and the tomato paste has turned darker in color, 1 minute. Pour in the wine to deglaze the pan, scraping up any brown bits. Let the wine reduce by half, about 2 minutes.

Stir in the chicken stock, sun-dried tomatoes, and Italian seasoning, and bring to a simmer. Once the sauce is simmering, add the chicken and any accumulated juices back into the pan; cook for 5 minutes. (The sauce should be thickened slightly.) Stir in the cream and parmesan, and let simmer for 5 minutes more to make sure the chicken is tender and all the flavors have melded.

Top with parsley and extra parmesan, and serve alongside mashed potatoes or any short cut pasta you like.