Combine the paprika, brown sugar, cumin, coffee, salt, pepper, onion powder, and garlic powder in a small bowl and stir to mix. Pat the meat dry with paper towels and rub the spice mixture all over.
Heat the olive oil in a large Dutch oven over medium-high heat. Sear the meat until nicely browned, 4 to 6 minutes per side.
Pour the beer over the meat, cover, and transfer to the oven.
Roast for 2 hours. Flip the meat over.
Add the garlic, parsnips, and carrots. Cover and roast until the meat and vegetables are tender, about 1 1/2 hours more.
Transfer the meat to a cutting board and let rest at least 15 minutes before slicing.
Transfer the vegetable and garlic to a platter, reserving the pan sauce.