Season the chicken with 1 tsp salt, 1/2 tsp pepper, and the paprika.
Heat the olive oil and 1 tbsp butter in a large skillet over medium-high heat.
Brown the chicken on both sides, 6–8 minutes per side. Transfer to a plate.
Add remaining butter. Sauté mushrooms until deeply browned, 5–6 minutes.
Stir in onion and cook until softened, 3–4 minutes. Add garlic and cook 30 seconds.
Sprinkle flour over the vegetables and stir for 1 minute to cook it out.
Deglaze with white wine, scraping up browned bits. Simmer until mostly reduced.
Whisk in broth, mustard, thyme, and remaining salt and pepper. Bring to a simmer.
Nestle chicken into the sauce. Cover and simmer gently 18–22 minutes, until cooked through.
Reduce heat to low. Stir in the cream and simmer uncovered 5–7 minutes to thicken.
Finish with lemon juice. Taste and adjust seasoning, then sprinkle with parsley and serve.