Season chicken liberally all over with salt and pepper.
Melt butter in a very large skillet or braiser (large enough for all chicken pieces to lay in 1 layer) over medium heat. Add chicken pieces, skin side down. Cook a minute or two; don't allow to brown.
Scatter onion all over and cook 30 seconds or so. Add garlic and stir around. Cook chicken and onions about 4-5 minutes, turning chicken pieces often in butter.
Sprinkle flour over all, turning chicken frequently to coat evenly. Add the vermouth, chicken stock, thyme and bay leaves. Add leeks and carrots, stirring them well into the other ingredients. Cover and cook over medium heat about 20 minutes. Check periodically to stir and prevent sticking. If sauce seems to be getting too thick, or things are starting to stick, add hot water, ¼ cup at a time and mixing well until slightly thinner and not sticking.
After chicken has cooked for a total of 30 minutes, add heavy cream. Simmer and stir a minute or two to combine well and heat through.¼ Serve with rice or mashed potatoes.¼