Combine the rub ingredients in a bowl.
Place the ingredients in a blender. Pulse until smooth. Set aside.
Combine the ingredients in a blender. Pulse until smooth. Refrigerate until ready to use.
Pat the chicken dry. Rub all over with the Southwest Rub.
Heat the Big Green Egg to 275F degrees, using the plate setter to cook over indirect heat.
Place the chicken on the rack, breast side up. Smoke for about 2 hours, until the meat reaches an internal temperature of 165F degrees.
Place in an aluminum pan and cover with foil. Rest for 30 minutes.
While it's resting, heat the BBQ sauce in a pot or microwave.
Pull the chicken, discarding the skin and bones. Toss in the warm sauce.
Split the Martin's Potato Rolls and grill cut side down, until slightly charred.
Pile sauced pulled chicken on bottom bun. Top with shredded lettuce and sliced red onions.
Smear chipotle crema on top bun. Place on top.