Melt 1 tablespoon of butter in a large, lidded nonstick sauté pan over medium heat. Add the bacon lardons and cook until they begin to brown and much of the fat is rendered, stirring frequently, about 5 minutes. Don't let it get too crisp—you want chewy little bites in the finished dish, not bacon bits. Don't worry if it's not cooked all the way through. It will finish cooking with the chicken. Transfer to a bowl with a slotted spoon.
While lardons are cooking, salt and pepper chicken generously on both sides. Add chicken to the bacon fat in the pan and brown on both sides, about 4 minutes to side. Transfer chicken to a plate. Pour off all but 2 tablespoons of fat in pan and reduce heat to medium low. (If you pour off too much fat—I did—drizzle in a little olive oil.) Add shallots and sweat until soft, stirring frequently to avoid browning, about 4 minutes. Add garlic to pan and cook until fragrant, about 45 seconds.
Turn off heat and deglaze pan with brandy, scraping up any browned bits. Add Riesling to pan. Quickly bruise thyme sprigs by rolling them with a rolling pin or the side of a glass. Add to pan, along with lardons. Bring mixture to a boil over medium high heat, add chicken to pan, cover and reduce heat to a simmer. Cook for 30 to 40 minutes.
Meanwhile, melt the remaining tablespoon of butter in another large skillet over medium heat and sauté mushrooms until they've released their juices and are nicely browned. Turn off heat and leave mushrooms in pan.
Transfer chicken pieces to a warm serving platter and tent with foil. Raise heat to medium high and slightly reduce liquid in pan, about 2 minutes. Discard thyme sprigs and add crème fraîche and mushrooms to pan and stir to combine. Cook until mushrooms are heated through. Spoon sauce and mushrooms over chicken and garnish with parsley. Serve immediately.
Alternatively, you can plate this dish. Spoon buttered egg noodles or rice on individual plates and top with a drumstick and thigh each and spoon sauce and mushrooms over chicken. Or serve chicken next to parsley potatoes.