Place water, 3 bottles beer, 2 onions, kosher salt, 1/2 cup brown sugar, curing salt, 1/4 cup pickling spice, and 2 tablespoons garlic in a very large pot. Stir well until salts are dissolved. Add beef; stir gently. Use a large bowl or heavy plate to keep the beef submerged. Cover with plastic wrap and refrigerate, stirring once a day, for 4 days.

Soak wood chips in apple juice for 2 hours.

Remove beef from pot, discarding brine, and rinse well under cold water. Let beef come to room temperature.

Preheat an outdoor grill to 150 to 175 degrees F (65 to 80 degrees C). Place soaked wood chips in a shallow aluminum pan on the heat source.

Place meat directly on the grate and allow to smoke for 2 hours.

Combine 1 beer, 1 onion, 2 tablespoons brown sugar, 2 tablespoons pickling spice, 2 tablespoons chopped garlic, and black pepper in a large saucepan; bring to a boil. Remove from heat and pour into a large roasting pan. Place beef in braising liquid in the roasting pan and cover tightly with aluminum foil.

Increase grill temperature to 250 degrees F (120 degrees C). Place the roasting pan on the grill and close the lid.

Roast the beef until tender, 3 to 4 hours. An instant-read thermometer inserted into the center should read at least 145 degrees F (60 degrees C).

Remove beef from the roasting pan, discarding braising liquid. Let beef cool until easily handled.