Step 1

Stir together first 6 ingredients; rub over all sides of pork shoulder. Wrap tightly in aluminum foil, and chill 1 hour or up to overnight.

Step 2

Preheat oven to 450°F. Unwrap pork; discard foil. Place pork shoulder, fat side up, in a large ovenproof Dutch oven, and cook, uncovered, at 450°F until lightly browned, about 45 minutes. Pour beer over pork shoulder; reduce temperature to 300°F, and cover with lid. Cook pork at 300°F, basting occasionally, until a thermometer inserted just next to (but not touching) bone registers 196°F and meat pulls easily from bone, about 2 hours.

Step 3

Remove pork from oven, and transfer to a plate. Remove and discard bone. Transfer cooking liquid to a 2-cup glass measuring cup. Let stand 10 minutes.

Step 4

Meanwhile, shred pork using 2 forks. Skim fat from cooking liquid. Return pork and cooking liquid to Dutch oven, and stir to combine. Serve with tortillas, avocados, and limes, or cover with lid to keep warm up to 1 hour.