In a large chef's pan or dutch oven, fry the lardons over medium heat until most of the fat has rendered out (but not until it's crisp). Transfer the lardons to a bowl with a slotted spoon.
You should now have a nice thick coating of brown "fond". This is what gives the dish much of it's depth. Remove 2 tablespoons of fat from the pan and set it aside in a small bowl. Add the chopped onion, celery and garlic and sauté until soft, scrapping the fond off the bottom of the pan so it doesn't burn.
Add the flour to the fat you've reserved and stir until there are no lumps. When the chicken is tender, transfer to a plate and tent with foil. Add the mushrooms and cipollini onions to the pan and turn up the heat to medium, simmering uncovered for about 15 minutes or until the onions are cooked and the sauce has reduced a bit. Add a few tablespoons of sauce to the fat/flour mixture and stir to make a slurry. Add the slurry to the sauce in the pan one spoonful at a time, mixing well after each addition to make sure there are no lumps. I don't like my sauce too thick, so I stopped about 2/3 of the way through, but if you like a very thick sauce, you can add all the roux. Salt and pepper to taste, then return the chicken to to pot to reheat and coat with the sauce.