In a blender, add all of your ingredients except the butter, broth, bay leaves, diced onions, tomato paste, roast (obviously), and the tortillas & cheese.
You've now made your barbacoa sauce.
In a large dutch oven pot, heat your butter on medium heat. Once it foams, add your onions. Allow them to brown and then add your chuck roast. Brown the roast on all sides. Once the beef is browned on all sides, add your barbacoa sauce by pouring it over the beef. Then add your chicken broth and your bay leaves. Cook on low heat (stirring intermittently) for four to five hours, this will help develop a rich flavor for your dish.
After about four or five hours, you should have a rich sauce and beef that comes apart easily with just a fork. If your sauce is too watery, slowly reduce the sauce so it thickens. Pull the beef apart in the sauce, this way the beef with soak up all the yummy flavors from the sauce. Once your barbacoa meat is ready, set aside 1/2 cup portions of the meat for the quesadillas.
Place a flour tortilla flat on your non-stick skillet. Add a thick layer of cheese on one half of the tortilla. Turn the heat up to high.
Then add your meat, then add another layer of cheese on top of the beef.
Fold the other half of the bread over and then press down on the quesadilla with a flat spatula. Cook for about 30 seconds to a minute (depending on how powerful your oven is).
This takes some practice to make sure you don't burn the quesadilla, but gently lift the bread up to see if it's burning (if you don't have the hang of it). Once you've flipped the quesadilla, the other side takes way less time, cook it for about 15 to 30 seconds and then remove it from the skillet.
Cut it in half and enjoy!