This chili took me about 6 years to perfect, and has won numerous awards. The best thing about it is that you can play with it. Add more of something, omit another. It's very versatile, and most importantly it provides a balance of salty, sweet, smokey, and tangy. It may seem like a lot of work, but it all pays off in the end. Trust me.
Start off by preheating your oven at 300 degrees. In a large baking pan (or two medium sized ones), place the lard or chicken fat in the pan and let it melt while the oven heats up. Rub the chicken with salt and pepper under and on top of the skin. Once the lard or fat is melted completely, place the chicken in the pan. You want the fat to be covering the chicken. Use a meat thermometer to monitor the temperature. You want them to be 165 degrees at the thickest part (legs will cook faster than thighs, in which case remove them when done and cover).
As the chicken is cooking, get started on chopping the squash, onions, garlic, and pepper. I like to spoon a little of the chicken fat from the pan to cook all the vegetables in. Cook the squash first in a wide pan or wok until cooked through.
In the meantime, you can get your big pot going on low heat with the beef broth, tomato paste, IPA, and salsa verde. Add the squash to the pot when cooked through. Then get started on cooking the chopped pepper and onion until just soft. Add the garlic and cook for another 1 minute until fragrant. Add these veggies to the pot.
Right around now the chicken should be cooked through (check temperature). Remove from oven and cover and let cool. While the chicken is cooling, chop the bacon into lardons and cook them until your desired done-ness, but not too crispy. Add the bacon to the pot with a slotted spoon. *Do not cover the pot completely as this creates too much steam and waters down the chili.* Now you're ready to get spicy!
In a non-stick pan over low-medium heat, add the cumin, coriander, allspice, cloves and star anise. Toast over the heat until fragrant, about 3 minutes moving the pan around. With a spice grinder, coffee grinder, or mortar and pestle - grind the spices until fine. Use a sieve to add the spices to the pot and avoid any big pieces going into the chili.
Remove the seeds from the New Mexico chiles and add them to the non-stick pan toasting as well. You want a bit of color, so toast for about 5 minutes. Break up and add to the grinder until fine. Pour through a sieve into the pot. Now, add the cinnamon, cocoa, rice vinegar, fish sauce, brown sugar, and hot sauce (if desired) to the pot as well. Give the pot of chili a good stir and make sure everything has blended nicely together.
Your chicken should now be ready for de-boning. Remove all tendons, bones, skin and excess fat from the pieces of chicken (*save these for stock!). Then chop the meat into nice small pieces. The key is to cut everything relatively the same size, that way nothing is over powering the other ingredients. Add your chopped chicken to the pot and cook for another hour over low-medium heat - OR - cook on low for a few hours.