Pre-heat your oven to 275F.
Brown the beef in the oil using an oven proof dutch oven large enough to hold the beef. You want the meat to brown up but not crazy brown. If you push it too far the edge of the beef will not get to the meltingly tender stage. This step is critical to getting the big beefy flavour so don't skip it.
Remove the beef from the pot.
Adjust your heat to medium low. Do not remove the fat in the pot. Pour the chili vinegar paste into the pan. It will bump so be ready. Stand back. Don't wear nice clothes for this step. Seriously.
Cook the chili vinegar paste for about 2-3 minutes, scraping up any browned bits on the bottom of the pot.
Add the chicken stock, stir to combine and return the beef to the pot.
Bring to a simmer.
Cover and place in the oven.
Cook (braise) the beef for about 4 hours total. Set a timer for 1 hour. After an hour remove the pot from the oven and flip the beef. Cover and return the pot to the oven. Repeat this a total of three times.
After 3 hours cooking time check to see if the beef is fork tender. I find it's about right at an internal temperature of 207F. It's ready when it's ready. Not before. If it's taking too long nudge the temperature up to 325F and check every 15-20 minutes.
If the beef is fork tender remove from the oven. If it isn't return the pot, covered, to the oven. Check every 20 minutes until it is fork tender.
Remove the beef from the pot. Let the beef cool until you can shred it. Two forks works for this. Your want the strands to be about 1 inch long so cut the beef before shredding.
Pour the liquid into a bowl. Skim the fat from the surface. If you have a fat separator kicking around from Thanksgiving use that.
Pour the defatted braising liquid (now a wonderful sauce) into the shredded beef and mix to combine.. Return the meat and liquid to the pot. Bring to a simmer and cook for around 5 minutes. This gets the sauce and the meat to really come together. Taste and adjust salt if required.
Serve and prepare to be told you make better than taqueria beef barbacoa!