Pat dry the chicken with kitchen towels, season with sauce and pepper on both sides.
Heat up a heavy bottomed pot over medium high heat, add in 2 Tbsp olive oil. When oil is hot, but not smoking, lay down 4 pieces of chicken breast, not overlapping. When one side is golden, flip them carefully to avoid splattering. When the other side is golden, take them out. Start cooking the other pieces in the hot oil. Make sure when doing this, the pan is not over crowded, otherwise the chicken breasts would just steam.
After all the pieces are seared, take them out and keep them somewhere warm.
Lower the heat to medium. Add in the butter, let it foam up. Then add the onion, stir around with a wooden spoon, and cook till the onion pieces are transparent, around 3 minutes.
Add the flour to the onions, stir till incorporated. The flour will eventually thicken the sauce.
Add mushrooms to the pot, stir them around with onions, and let them cook for 2 minutes. Stir in the chopped garlic. Give them another stir and let cook for 2 more minutes. Mushrooms should be fragrant and tender.
Pour in madeira wine, chicken broth. Let them cook for around 3 minutes till they reduce to half the volume.
Add in heavy whipping cream, bring it to a boil. Check the seasoning and add more salt if needed.
Add the chicken breasts back into the sauce. Let them heat up and absorb the beautiful sauce you just made. Simmer for 2 minutes.
10. Garnish the dish with some green, fresh chopped parsley.
Video
Notes
Use an internal thermometer to prevent overcooking! Omit wine if serving to children, although some say alcohol cooks out, other say it doesn't.