Place chicken breasts between two sheets of plastic wrap and pound to an even 1-inch thickness using a meat mallet. Season both sides generously with salt and black pepper.

Heat 1 tbsp butter and olive oil in a 12-inch skillet over medium-high heat until butter melts and shimmers. Add chicken and sear 4 to 5 minutes per side until deeply golden and internal temperature reaches 165 degrees F. Transfer to a plate to rest.

Reduce heat to low. Add remaining 2 tbsp butter to the same skillet. Once melted, sprinkle in flour and stir constantly for 1 minute to build a light roux.

Pour in chicken broth and scrape up all browned bits from the bottom of the pan with a wooden spoon.

Add milk, sour cream, onion powder, garlic powder, Italian seasoning, and ranch seasoning mix. Whisk until smooth and fully combined with no lumps.

Return chicken and any resting juices to the skillet. Spoon sauce over the chicken and simmer on low for 3 to 5 minutes until sauce coats the back of a spoon. If too thin, simmer 2 to 3 more minutes. If too thick, whisk in a splash of milk. Garnish with parsley and serve immediately.