Step 1Drain the beans and put them in a large saucepan. Add enough water to just cover them. Wrap the garlic, carrot, celery, chile pods, thyme, sage and bay leaves in a doubled piece of cheesecloth and tie it closed with kitchen twine. Add the bundle and the onion to the pot with the beans, stir in the olive oil and salt, and bring the water to a boil over high heat. Reduce the heat and very gently simmer the beans, stirring from time to time, until they are very tender and creamy, adding more water to the pot if the beans begin to be exposed, about 1 to 2 hours (timing will vary depending on the type and age of the beans). Taste the beans for doneness; they should be creamy in texture without any chalkiness or dryness. Remove from heat, discard the cheesecloth bundle and onion, and set the beans aside to cool in the cooking liquid.
Step 1Put the tomatillos in a single layer in a cast iron skillet (do this in batches if needed) over medium-high heat and scatter the garlic cloves around them wherever there is room in the pan. Toast the tomatillos, turning as needed, until they are charred on all sides and bursting, releasing their liquid. The garlic should be soft on the inside; move the garlic as needed to cooler spots on the pan so the cloves can cook and soften without burning. Remove the garlic cloves from the pan and set aside until they're cool enough to touch, then peel them. Remove the tomatillos from the pan as they're done and put them on a plate or in a bowl to cool slightly before puréeing them.
Step 2Increase the heat under the skillet to high and heat until the pan is searing hot. Add the chiles (in batches if needed) and roast until charred on all sides. Place the chiles in a sealed plastic bag to steam until cool enough to handle, then rub off the peels and remove the cores and seeds (do not rinse the chiles, as this will remove flavor).
Step 3Tear off the leafy portion of the cilantro bunches and discard the long stems. (The short, delicate stems that have leaves on the ends of them are fine.) In the bowl of a blender (do this in batches as needed), purée the tomatillos, chiles and garlic. Pulse the blender a few times, then add the cilantro and purée until smooth. Set aside.
Step 4In a large Dutch oven or another heavy-bottomed pot, add the oil and heat it over medium-high heat until hot. Add the turkey, sprinkle it with 2 teaspoons of the salt and cook for about 5 minutes, breaking it up with a wooden spoon until only a tiny bit of pink, raw meat is visible. Add the onions, leeks and celery. Sprinkle with the remaining 2 teaspoons of salt and cook, stirring often, until the vegetables soften but don't brown, 8 to 10 minutes.
Step 5Stir in the the puréed charred vegetables, the beans and 2 cups of the bean cooking liquid. Add enough chicken broth to just cover the chili. Reduce the heat and gently simmer the chili until it is thick and soupy (texture of rich, thick chili), adding additional bean liquid and/or chicken broth to the pot as necessary to keep the chili covered with liquid, about 2 hours. Taste for seasoning and add more salt if desired.
Step 6Set aside to cool, then cover and refrigerate if not serving right away. The chili will continue to thicken as it sits; add additional liquid when reheating as desired. Serve the chili with crema, queso fresco and green onion on the side for garnishing.