Heat oil in a large oven-proof skillet. Mix rosemary, thyme, salt and pepper together in a small dish. Sprinkle on chicken thighs and add to hot oil. Heat chicken on both sides, about 5 minutes each until browned. Remove from heat.
Cook chicken in oven, about 15-25 minutes or until center is done. Remove from pan and set aside and keep warm.
Add mushrooms to pan and book for about 4 minutes or until tender. Stir in flour and mix well. Add broth and mustard and mix well, heating, on medium heat until bubbly and thick.
Return chicken to pan for 2 minutes, and serve chicken with sauce and mushrooms.