Remove the giblets from the chicken. Discard the liver (it makes the broth bitter) and hold onto everything else. Rinse the chicken with cool water. Put the chicken, onion, and giblets in a large stockpot. Pour in enough cold water just to cover by 1 inch (about 3 quarts). Toss in the garlic and herbs and allow the water to slowly come to a boil over medium heat. Skim off the foam then reduce the heat and simmer gently for 1 hour, uncovered, until the chicken is cooked through. Skim any impurities that rise to the surface; add more water if necessary to keep the chicken covered.
Carefully remove the chicken to a cutting board and let it cool. With a slotted spoon, remove the vegetables, giblets, thyme and bay leaf from the pot and discard. Reserve chicken broth. When the chicken is cool enough to handle, discard the skin and bones; shred the meat by hand.
Meanwhile, seed, core, and thinly slice the poblano peppers.
Heat a 2-count of olive oil in a medium saucepan over medium heat. Add the onion and garlic and cook until softened, about 5 minutes. Dust the vegetables with the ground cumin, coriander, and oregano, and stir; cook 1 minute. Stir in the ground tortillas. Pour in the reserved chicken broth, season with salt and cook 20 minutes. Now add the shredded chicken and chiles, and the cilantro and cook 5 more minutes. Taste for seasoning.
To serve, ladle the chili into big bowls and garnish with grated cheese, cilantro, and a wedge of lime. Serve with the Smoky Chile Cornbread.
Preheat the oven to 350 degrees F.
Put the bacon into a cold 10-inch cast iron pan and cook over medium heat until the fat is rendered and the bacon bits are crisp, 5 to 7 minutes. Use a slotted spoon to remove the bacon to a paper towel lined plate. Keep the bacon fat in the pan and set aside.
In a large bowl, whisk together the cornmeal, flour, baking powder, sugar, baking soda, and salt. In a separate bowl beat the eggs with a whisk until foamy; whisk in the milk. Add the milk mixture to the dry ingredients and stir just until combined. Fold in the bacon bits, chile, and chives. Pour the batter into the cast iron pan. Bake until a toothpick inserted in the center comes out clean, about 20 to 25 minutes.