I find that the chorizo, which is kinda runny, is a perfect start to the chili, as it's often very fatty. Bacon works great, too.
I like beans in my chili, but you can skip if you feel strongly about it -- talkin' to you, Texans! You can also use canned beans, and if you are, add them towards the end of cooking. Be sure to rinse the canned beans before adding to remove some of the starchy liquid they're canned in.
Don't get all hung up on an exact combination of dried Mexican chiles. Just be very sure to use mostly ancho, pasilla and guajilllo chiles, as they are not too spicy. Hatch green chiles are great, too, but they are hotter.
Serve this over rice or polenta, garnished with cilantro and maybe some Mexican queso seco, jack cheese or American cheddar.
If you want to go full Mexican here instead of Tex-Mex or Southwest, try my recipe for chile colorado, which is a lot like chili, but is more authentically Mexican.
Soak beans in water overnight. If you have forgotten this, pour boiling water over them and soak for 4 hours, changing the water after 2 hours.
Break up and seed the chiles and cover with boiling water. Let stand for an hour or so. Grind to a puree with the consistency of gravy, adding about 1 cup of the soaking water and the coffee to do so.
Break up the chorizo or chop bacon and fry over medium heat in a Dutch oven or other large, lidded, oven-proof pot. Once the chorizo has browned or the bacon is crispy, remove it and set aside. Add the venison and brown over high heat. You want the highest heat on your most powerful burner here, because the meat will want to steam and stew and not brown. If you are doing a big pot of chili, brown the meat in batches. Stir occasionally as it browns. Salt it as it cooks.
Once all the meat is ready, add the onion to the pot and cook for 5 minutes, stirring often. If you are using chorizo, return it to the pot; if you are using bacon, leave it out for now. Add the garlic, stir and cook for 1 minute. Add the beans, paprika, cumin, coriander, chipotle powder and salt one at a time, stirring to combine each time.
Add chile puree and tomato paste and stir to combine well. Add the molasses and enough beef broth to cover everything – you want it to be thin like a soup. I typically need at least a pint of broth, sometimes a quart. Stir to combine all this well, bring to a bare simmer and cook gently for 3 hours or so, stirring occasionally. Put the lid halfway over the pot as it cooks. You want it to eventually cook down and be thick.
Once the beans are tender, you're good to go. If you are using canned beans, now's the time to add them. Return the bacon to the chili if you're using it. Serve the chili with rice or cornbread, and top with cilantro, cheese and maybe some pickled onions.