In a large skillet, heat olive oil over medium-high heat. Season chicken with salt and pepper, then add to the pan. Sear until golden and just cooked through, about 5–7 minutes. Transfer to a plate and set aside.
In the same skillet, reduce heat to medium. Add butter and sauté the chopped onion until soft, about 3 minutes. Add garlic and mushrooms and cook until the mushrooms are browned and their liquid evaporates, around 5 minutes.
Sprinkle flour over the mushroom mixture and stir to coat. Cook for 1 minute to remove the raw flour taste. Slowly pour in the chicken broth, stirring constantly until smooth and slightly thickened.
Stir in the sour cream and Dijon mustard until well combined. Return the chicken to the skillet and simmer for another 3–5 minutes, until heated through and coated in the creamy sauce. Adjust seasoning with salt, pepper, and paprika (if using).
Spoon the stroganoff over egg noodles, rice, or mashed potatoes. Garnish with fresh parsley and serve warm.