Preheat the oven to 275°F. (No need to preheat the oven if you're utilizing a slow cooker)
Generously salt the outside of the chuck roast and set aside.
Heat the dutch oven or braiser over medium-high heat. Add ½ of the oil to the pan and allow to heat. Caramelize all sides of the onions then remove and set aside. Repeat with the halved tomatoes.
Add the remaining oil to the pan and sear the chuck roast on all sides. Remove and set aside with the caramelized onions and tomatoes.
Deglaze the pan with 1 cup of the beef broth and the tablespoon of white vinegar, using a wooden spoon to loosen all of the brown bits from the bottom of the pan.
If using a slow cooker, follow the steps in the notes section. If using a dutch oven or braiser, continue to follow the remaining instructions below.
Turn the heat off and add the onions, tomatoes, canned tomatoes and green chiles, the chipotle peppers in adobo, clove, and oregano to the dutch oven or braiser and stir just to combine. Nestle the chuck roast into the pan and add beef broth until 1/3 of the chuck roast is exposed.
Add the bay leaves and head of garlic with the open top facing up.
Cover with the lid and place in the oven to cook for 3 hours or until the meat is tender and easily shreds.
Once your meat has cooked, carefully remove the meat and the head of garlic from the dutch oven and set aside. Remove and discard the bay leaves.
To a blender, add the remaining contents of the dutch oven. Once cool enough to touch, squeeze the head of garlic to push the soft cloves out and into the blender. Blend until smooth. Taste, add salt if necessary.
Add the chuck roast back to the dutch oven and shred with tongs or forks then add the desired amount of sauce back to the meat. Bring up to a simmer and your birria is ready to be served as tacos, burrito bowls, or on it's own as a beefy Mexican stew.
Store any leftover sauce in an air tight container in the fridge for up to 1 week.