Season chicken strips with salt and pepper. In a large skillet over medium-high heat, heat 1 tablespoon of olive oil. Add chicken in batches, searing until golden and cooked through. Remove and set aside.
In the same skillet, add remaining oil and sauté diced onion until translucent, about 3 minutes. Add garlic and mushrooms and cook until mushrooms release their juices and brown, about 5–7 minutes.
Sprinkle flour over the mushroom mixture and stir to coat. Cook for 1 minute to remove the raw flour taste.
Pour in chicken broth, scraping up any browned bits. Stir in Dijon mustard, Worcestershire sauce, and simmer for 2–3 minutes until slightly thickened.
Reduce heat to low. Stir in sour cream and heavy cream (if using). Return chicken to the pan and simmer gently for another 3–4 minutes, allowing flavors to meld.
Serve hot over egg noodles, rice, or mashed potatoes. Garnish with fresh parsley.