Place all of the poaching ingredients in a pot, cover with water and bring to a boil. Add salt and simmer at low, rolling boil for 1 hour turning chicken with tongs once. Turn off heat and let chicken cool completely in its own juices.
Discard skin and bones and slice chicken into thick pieces; reserve. (You will have more stock than needed for this recipe, store in fridge for other uses for 1 week or freeze in container for up to 6 months.)
Heat a deep skillet with tight-fitting cover over medium-high heat. Add oil; when it smokes, add bacon and brown. Set aside on a plate. Add mushrooms and brown. Melt in butter and add shallots, garlic, salt, pepper, thyme and dill, and cook to soften, 7-8 minutes more. Sprinkle in flour and stir a minute or 2 more, add poaching liquid and bring to a bubble. Thicken a bit make a loose gravy. Add in carrots and simmer 2-3 minutes. Add in haricot verts and reserved chicken.
Whisk up flour, baking powder, salt, pepper and nutmeg, and stir in eggs and buttermilk. Drop heaping tablespoon dumplings into chicken and gravy, cover pan and steam cook the dumplings 8-10 minutes.