Pat the chicken breasts dry with kitchen paper and season both sides with salt and black pepper.
Heat the olive oil and butter in a large frying pan over medium-high heat.
Cook the chicken for 5–6 minutes per side until golden brown and fully cooked. Remove and keep warm.
In the same pan, cook the chopped onion for 3–4 minutes until soft.
Add the garlic and mushrooms and cook for another 2–3 minutes.
Sprinkle in the plain flour and stir for 1 minute.
Pour in the white wine and stir until smooth. Simmer for 2–3 minutes to cook off the alcohol.
Add the chicken stock, Dijon mustard, thyme, and double cream. Stir until the sauce becomes smooth and creamy.
Return the chicken to the pan, spoon the sauce over it, and simmer for 5 minutes.
Sprinkle with fresh parsley and serve immediately with your favorite side dishes.