Two to three hours prior to cooking, rinse the chicken quarters under cold water and pat-dry thoroughly with paper towel. Season each piece with salt and pepper on both sides and roll in flour. Set aside, at room temperature.

Heat up a large frying pan (or skillet) over medium heat with the butter and extra virgin olive oil. When the butter is sizzling, place the chicken quarters in, skin-side down. Cook for about 10 minutes, without touching, until the chicken skin is golden brown and the chicken is ¾ done; just firm. Flip the chicken pieces and cook for 10 more minutes. Transfer the chicken to a plate and cover with foil. Keep the pan hot and do not rinse it (keep the chicken drippings in).

Add the shallots and garlic to the pan. Cook for about 5 minutes, stirring occasionally, until the shallot is lightly caramelized. Add the mushrooms and cook for about 10 minutes, stirring occasionally until the mushrooms are almost done. Pour in the white wine and chicken stock, and nestle the chicken pieces back into the pan, with the mushrooms all around. Cover with a lid and cook for 30 minutes on medium-low heat.

Remove the chicken pieces, and add the crème fraiche to the mushroom sauce. Stir to combine and place the chicken pieces back into the pan. Cook for 10-15 minutes (no lid), until the sauce thickens to creamy consistency.

Serve immediately over rice, pasta and/or green beans.