Have a pot of water simmering on the stove for the pasta.

If the chicken breasts are overly thick, pound them until slightly flattened. Sprinkle both sides of the chicken with the salt and pepper, then dredge in the flour.

In a large skillet, heat 1 tablespoon of the butter and 2 tablespoons of the oil over medium heat. Fry 2 chicken breasts at a time until golden brown on both sides, about 3 minutes on each side. Remove the chicken to a plate. Add the remaining tablespoon of butter and remaining 2 tablespoons of olive oil. Repeat with the remaining chicken breasts.

After removing the chicken, lower the heat to medium-low. Pour in the wine, chicken broth, and lemon juice. Whisk the sauce, scraping the bottom of the pan. Increase the heat to medium and allow the sauce to cook, bubble, and thicken until reduced by about half or two-thirds. Sprinkle in a little salt and pepper as it's cooking.

Reduce the heat to low and pour in the heavy cream. Whisk the sauce together and allow it to cook until the sauce thickens and coats the surface of a spoon, 1 to 2 minutes. Taste and adjust the seasonings or other ingredients.

Right at the end, cook the pasta until al dente—do not overcook!

Using tongs, place a medium-sized mound of pasta on a plate. Place a cooked chicken breast beside it, then spoon the sauce over the chicken and the pasta. Sprinkle a little more parsley over the top.