Cut the beef chuck roast into large chunks. Heat olive oil in a skillet over medium-high heat until shimmering, then sear the beef pieces until golden brown on all sides. This step locks in the flavor and creates a crust on the meat.
Next, transfer the beef into a slow cooker or Dutch oven. Add the chopped onion, minced garlic, vinegar, lime juice, and beef broth. Sprinkle in all the spices, including cumin, oregano, paprika, and chipotle powder. Stir everything to coat the beef evenly.
Cover and cook the barbacoa on low for 6-8 hours (or on high for 4 hours), until the beef becomes tender and easily shreds with a fork. If using a Dutch oven, cook in the oven at 300°F for 4-5 hours.
Remove the cooked beef from the pot and shred it with two forks. If you like crispy edges, spread the shredded beef onto a baking sheet and broil in the oven for 5-7 minutes. This extra step will give the barbacoa a delicious texture.
Warm the corn tortillas in a skillet or wrap them in foil and heat in the oven. Place a generous amount of barbacoa onto each tortilla and top with fresh mango pico de gallo, cilantro, and onion. Squeeze a wedge of lime over the top before serving.