Cut the chicken into 16 pieces; 6 pieces of breast, 4 pieces of thigh, 2 legs, 4 pieces of wings. (If you are using 2 chickens, cut each into 8 pieces.) Lay chicken pieces on a cutting board, season with salt and pepper and a light dusting of flour. Turn the pieces over, season and dust with flour.
Melt 2 tablespoons of the butter in each of two large skillets over medium-high heat. Divide the chicken between the skillets by dark and light meat. Brown the chicken on all sides for about 15 minutes. Add half the onions and garlic to each skillet and cook for a few minutes. Reduce the heat to low, then add 1 cup Riesling to each skillet. Cover each skillet loosely with a piece of foil and cook until the juices run clear when the chicken is pieced with a sharp knife, about 45 minutes. (The white meat may only take 30 minutes to cook so keep an eye on it.) Transfer the cooked chicken and onions to a large platter and keep warm in a very low oven. Use a rubber spatula and transfer all the pan juices from both skillets to a small bowl.
Melt the remaining 4 tablespoons of butter in one of the skillets over medium-high heat. Add the mushrooms, toss in the butter and cook until lightly browned, about 15 minutes. Add the lemon juice and season with salt and pepper. Use a slotted spoon to transfer the mushrooms on top of the chicken. Stir the pan juices into the skillet over medium heat. Add the cream and stir until hot and bubbly. Pour through a strainer over the chicken. Serve garnished with herbs, if you like.