There are two types of chorizo and it is important not to confuse them as one needs to be cooked and the other doesn't. Mexican chorizo is moist and needs to be cooked. Spanish and Portugese chorizo are dry-cured and do not need to be cooked. Both kinds are heavily seasoned with vinegar, garlic, cumin, oregano, and chillies. Mexican chorizo often is spiked with Tequila.

Chorizo is a sausage, flavored most notably with garlic and chiles, and sometimes cumin, and can be purchased like other sausage, stuffed into casings, or just in bulk, like ground beef. It originally came from Spain and Portugal (where it is known as chouriço), and was introduced to Mexico by the Spaniards, but has evolved into its own version using more local flavors and ingredients.

It can be made with either beef or pork, and there are differences between Mexican and Spanish/Portugese versions - notably that while the Mexican version uses fresh pork, the Spanish version instead uses a smoked/cured pork, enabling it to be used without cooking. There is also a Salvadorean version that uses sweeter spices than the Mexican version. (thanks sbeitzel)

The town of Toluca, about 40 miles to the west of Mexico City, is famous for its chorizo, and the Mexican state of Sonora in general makes it very well.

Recipe for Mexican Chorizo:

Meat:
1 lb. boneless pork shoulder (as fatty as possible) - in 1/2 inch cubes

Chiles:
5 ancho chile peppers
1 pasilla chile pepper

OR

1/2 cup chili powder (if you don't have/don't want to deal with fresh chiles)

Spices:
2 cloves
3/4 inch cinnamon stick
1/4-1/2 tsp oregano
1/4-1/2 tsp marjoram
1/4-1/2 tsp thyme
1 bay leaf
3/4 tsp salt

OR

1 Tbsp dried Oregano
1 tsp whole cumin seed, crushed
1/2 tsp freshly ground black pepper
3/4 tsp sugar

Misc:
2-3 cloves garlic, minced
2 Tbsp red wine vinegar
2 Tbsp cider vinegar

Take the cubed pork, and put in the freezer for about 15-20 minutes - it should just be starting to freeze at that point.

Simmer the chiles in water, about 15 to 20 minutes, to make them very soft, then run them under cool water, and remove the stems and seeds (some seeds can be left if you want the sausage spicier). Remove the flesh from the skin - a food mill works well for this - and process the flesh into a pulp. If you are just using chile powder, just add some water to the powder to make a dry paste.

Take the spices, grind (if necessary), and mix together into a powder.

Take 1/4 cup of the chile pulp, and mix with the pork, rubbing the pulp into the meat by hand (gloves are recommended due to the chili peppers). Add the spices and garlic to the meat, and mix well.

Put the meat into a food processor, add the red wine and cider vinegar, and start pulsing the processor to grind up the meat. Keep going until the meat is ground to the desired amount.

Refrigerate for at least overnight to allow the flavors to seep into the meat.

Note that you can use ground pork for the recipe - you can simply mix the spices and such with the meat, and avoid the freezing/processing of the cubes.

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