Use a meat mallet to pound each chicken breast to an even 1-inch thickness. Pat the chicken dry with paper towels, then season both sides generously with salt and pepper.

Heat 1 tablespoon of butter and the olive oil in a 12-inch skillet over medium-high heat until the butter foams. Sear the chicken breasts for 4-5 minutes per side until golden brown. The internal temperature should reach 165°F. Transfer to a plate and tent with foil.

Reduce heat to low and add the remaining 2 tablespoons of butter to the skillet. Once melted, stir in the flour and cook constantly for about 1 minute until it forms a golden paste.

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

Stir in the milk, sour cream, onion powder, garlic powder, Italian seasoning, and ranch seasoning mix. Whisk continuously until the sour cream fully incorporates and the ranch seasoning dissolves into a smooth sauce.

Return the chicken and any accumulated juices to the skillet. Spoon the sauce over the chicken and simmer for 5-7 minutes until the chicken reaches 165°F internally and the sauce thickens enough to coat the back of a spoon. If sauce gets too thick, add a splash of milk. Garnish with fresh parsley if desired and serve hot.