Below is a chorizo recipe I've used numerous times with excellent results. It's a fairly authentic recipe but called Oaxacan-"Style" only because of the chiles used. Traditional Oaxacan chorizo call for chiles that are indigenous to the area and not found elsewhere in Mexico, much less the U.S. There are a few importers in the U.S. that offer the traditional chiles, but at prices that run $10-$20 an ounce. The chiles called for in this recipe are ones that are readily available and most closely approximate the traditional ones. Also note that this is a "Base" recipe calling only for 1 lb. of meat. It's proportionally scalable up and I never make less than 5 lbs. when preparing it.
You'll want about 2 1/2 oz of whole dried chiles (anchos, guajillo, chipotle or another mixure of fairly mild to medium warm chiles). If using ground chiles only (not recommended), substitute with about 1 1/2 oz. Keep the meat very cold at all times to improve the grinding and stuffing process.
Oxacan-Style Chorizo
6-7 ounces pork belly
9-10 ounces pork shoulder
2 or 3 medium ancho chiles, seeded and stemmed
1 to 2 guajillo chiles, seeded and stemmed
1 to 2 dried chipotle chiles, seeded and stemmed
1/2 teaspoon black peppercorns
2 whole cloves
1/2 inch cinnamon stick (preferably canela)
3/4 teaspoon Mexican oregano or marjoram
1/4 teaspoon thyme
generous pinch ground nutmeg
2 teaspoons smoked paprika (Spanish Pimenton de La Vera preferred)
1/2 teaspoon cayenne pepper
2 1/4 teaspoons kosher salt (Mortons. If using Diamond Crystal kosher salt use 3 teaspoons)
1 garlic clove, whole
1 garlic clove, minced
1/3 cup cider vinegar
water for soaking chiles
Hog casings
Kitchen twine
Cut the pork belly and shoulder into finger shaped pieces 2 to 3 inches long (remove any tough or stringy gristle). Coarsely grind the meat with a meat grinder. Place into the refrigerator to chill while you prepare the seasonings.
Tear the chiles into large, flat pieces. In a hot, dry pan, quickly toast the chiles a few pieces at a time, just until they start to change color and/or blister. This will only take a few seconds - do not overcook or burn. Place the toasted chiles into a bowl, cover with hot water and soak until softened, about 20 minutes.
Place the peppercorns, cloves, cinnamon, oregano and thyme into a spice grinder and grind finely. If you do not have a spice grinder, add these to the blender in the next step, but run it much longer.
Drain the chiles (reserving the liquid) and place into a blender along with the ground spice mixture, the nutmeg, paprika, cayenne, salt, and 1 garlic clove. Add the vinegar and 5 tablespoons of the reserved chile soaking liquid, then blend until smooth.
Using a large spoon, thoroughly mix the seasoning and minced garlic into the ground meats. It will be quite loose. Cover and refrigerate overnight.
Prepare hog casings for stuffing by soaking in warm water at least 30 minutes. Change the soaking water and run fresh water through them to remove traces of salt. Stuff the meat into the casings, but leave each piece of casing unstuffed at least 6 inches at each end. Keep the long sausage link quite loose rather than densely packed (if too tight, the casing may burst while creating the small links). Starting in the center and working toward the ends, use kitchen twine to tie the sausage into short, tight rounds the size of a golf ball.
Hang the links in a cool airy place (50-60 degrees) for 36-48 hours or until they have firmed up and are dry to the touch. Be sure to put a baking tray lined with paper towels underneath the sausage to catch the drips. Cut the finished sausage into shorter sets of links, then wrap in plastic and refrigerate or freeze until ready to use.