Served with roasted potatoes and steamed broccoli.
Rub each piece of chicken in salt and pepper mixture.
About 40 minutes before serving, start the potatoes: heat the oven to 425°F. Cut the potatoes into bite-size pieces, toss with the olive oil, salt and pepper, and roast for 25–30 minutes until golden, turning once. If the oven is already in use at a lower temperature, roast on another rack and allow 10–15 minutes longer.
Heat oil and melt butter in deep-sided, 12-inch (~30 centimeter) sauté pan on medium-high heat. When the oil is hot, but not smoking, use tongs to add chicken skin side down.
Brown both sides until skin is golden brown and chicken is cooked, about 12-15 minutes. Remove chicken to a platter and cover loosely with aluminum foil to keep warm.
Pour out half of oil from pan, and use other half to brown shallots over medium-high heat. Slowly add vinegar and boil until reduced to almost a syrup. Add crème fraîche/cream and cook until blended and brown, about 5 minutes. Return chicken to pan to coat and heat.
Steam or microwave the broccoli until tender, about 5 minutes, then toss with the butter, a squeeze of lemon and a pinch of salt.
Return chicken to platter. Add garnish if available, and serve.