Pulled pork is usually made using the pork butt, sometimes called the pork shoulder or Boston Butt, and is cooked over low heat, often in a smoker, for several hours. Using sous vide takes longer but you don't have to manage a fire or look in on the meat. My favorite combination is probably 156°F (68.8°C) for around 18 to 24 hours, it's shreddable but not over-tender.
For a more traditional flavor, you can either pre- or post-smoke the pork shoulder, just make sure it is cold when you are smoking it. I like to serve it with traditional BBQ sides such as corn on the cob, coleslaw, or macaroni and cheese.
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Preheat a water bath to 156°F (68.8°C).
If the pork shoulder is too large to fit into a bag, cut it into multiple pieces. Mix the spices together in a bowl then coat the pork with them. Place the pork in a sous vide bag then seal. Cook the pork for 18 to 24 hours.
For more information on the cooking times you can read my detailed article which addresses why is there a range in sous vide cooking times.
Take the chili peppers and soak them in water for 30 minutes. Remove the stems and seeds.
Heat some olive oil in a pan over medium heat, add the tomato paste then cook until just starting to darken. Add the chili peppers and remaining ingredients and blend well. Bring the mixture to a simmer and let cook for at least 5 minutes for the flavors to meld, or up to 30 minutes if you want it thicker. If you prefer a thinner sauce, add more water until it is the desired consistency.
Remove the pork from the sous vide bag and shred it with a fork and tongs.
On a plate, make a pile of the pulled pork and top with the chili pepper BBQ sauce. Serve with your favorite BBQ sides.
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