In a small mixing bowl, add all the spice rub ingredients and stir to combine. Set aside.
Move the oven rack to the top position and turn the oven broiler to high. (*Note 5)
Pat dry the chuck roast with paper towels and coat with the beef bouillon paste. Evenly coat the roast with the spice rub, using your hands to press the spices into the paste, and transfer to a roasting pan. Save any excess spice rub (you'll use it later).
Place the pan under the broiler and let the roast sear for 5-8 minutes, until the outside is dark brown and crusty. Keep your eyes on it, as it can quickly burn.
Remove the roast from the oven and reduce the oven temperature to 300°F. Add the beef consommé, rotel, lime juice, brown sugar, oregano, and remaining spice rub to the pan. Use a small spatula to stir the ingredients together. Add the onions and bay leaves to the liquid.
Tightly cover the roasting pan with aluminum foil and transfer the pan to the oven. Bake for 3½-4 hours, or until fork tender. Check at the 3½ hour mark, to see if it shreds easily with two forks. If not, bake for another 30 minutes, or until it does easily shred.
Remove the roasting pan from the oven and let rest, still covered, for 10-15 minutes. When ready to serve, remove the foil and use two forks to shred the roast right into the juices.
Give the shredded beef a final stir and taste, adding additional salt if needed. Drain the meat of excess liquid before using.
SLOW COOKER
In a small mixing bowl, add all the spice rub ingredients and stir to combine. Set aside.
Pat dry the chuck roast with paper towels and coat with the beef bouillon paste. Evenly coat the roast with the spice rub. Save any excess spice rub (you'll use it later).
Heat the vegetable oil in a large cast iron skillet over medium-high heat. Once hot, add the beef and sear on all sides. Remove and transfer to the slow cooker.
Add the beef consommé, rotel, lime juice, brown sugar, oregano, and remaining spice rub to the slow cooker. Use a spatula to stir the ingredients together. Add the onions and bay leaves to the liquid.
Cover and cook on high for 3 ½ – 4 ½ hours or on low for 6-8 hours, or until the beef shreds easily with two forks.
Use two forks to shred the beef directly in the slow cooker. Give the shredded beef a stir and taste, adding additional salt if needed.
Cover and let cook on warm (or low) for a final 20 minutes. Drain the meat of excess liquid before using.
Notes
Note 1 – If you don’t have beef bouillon, use vegetable or avocado oil instead.Note 2 – Beef consommé has a much stronger flavor profile than stock, so I highly recommend using it. It does tend to be saltier, however, so I wait to add more salt until after cooking.Note 3 - Any flavor rotel will work. Note 4 - Use regular oregano if you don't have Mexican oregano.Note 5 – If using a dutch oven you may need to place the oven rack in the second position as they’re much taller than a roasting pan.