Pat thighs dry, season with salt and pepper. Heat oil in a large skillet over medium-high.
Brown chicken 4-5 minutes per side until golden. Transfer to a plate.
Add butter and mushrooms to skillet; cook 4 minutes until soft.
Stir in garlic for 30 seconds then pour in broth, scraping browned bits.
Whisk in cream and Dijon, bring to a simmer.
Return chicken to skillet, spoon sauce over, reduce heat to low.
Cover and cook 8-10 minutes until chicken reaches 165°F.
Sprinkle parsley and serve over rice or noodles.