Season both sides of the chicken with salt, pepper, and Italian seasoning.
Heat olive oil and butter in a large skillet over medium heat.
Add the chicken and sear for about 4-5 minutes on each side until golden brown and cooked through. Remove and set aside.
Sprinkle flour into the skillet and whisk for 1 minute.
Gradually stir in chicken broth, then add half and half, sour cream, and ranch seasoning. Whisk until smooth.
Bring to a gentle simmer and let cook for 3-4 minutes until slightly thickened.
Add shredded cheese and stir until melted and creamy.
Return the chicken to the skillet, spoon sauce over the top, and simmer for 2-3 more minutes.
Garnish with fresh parsley and serve.