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