Pound the chicken breasts to an even 1-inch thickness using a meat mallet and season both sides with salt and pepper.
In a skillet over medium-high heat, melt 1 tablespoon of butter and add the olive oil. Sear the chicken on each side until golden brown, about 4-5 minutes per side. Remove to a plate and set aside.
Reduce heat to low and add the remaining butter. Stir in flour and cook for about one minute.
Pour in chicken broth and scrape up the browned bits stuck to the pan.
Add milk, sour cream, onion powder, garlic powder, Italian seasoning, and ranch seasoning mix. Stir to combine until the sour cream and ranch seasoning have fully dissolved into the sauce.
Add chicken and plate juices back to the pan and spoon the sauce over the chicken. Simmer until the chicken is heated through and the sauce has reduced slightly.
Dish and serve hot, topped with fresh parsley if desired.
Notes
Use boneless, skinless chicken breasts on the smaller side (5-8 oz each); if using large breasts, cut in half lengthwise to make 4 cutlets. Use full-fat sour cream so it doesn't curdle in the sauce. For extra flavor, top with bacon bits or stir them into the sauce. Leftovers keep in the fridge for 3-4 days; reheat with a splash of milk or broth to loosen the sauce.