Blend cayenne pepper, garlic powder, onion powder, sugar and salt; rub on pork shoulder. Grill over low heat or bake at 275° F for 1-1/2 hours.
Transfer pork to saucepot. Pour barbecue sauce over pork. Cover and simmer until fork tender. Remove from sauce; cool pork slightly, then shred. Reserve 3/4 cup sauce.
Melt butter in large nonstick pan; add jalapeño and cook for 1 minute over medium heat.
Add eggs. Cook and scramble until eggs are firm throughout with no visible liquid egg remaining.
Spoon 2 oz. pulled pork and 1/4 cup eggs onto a lettuce leaf. Top with 1 tablespoon reserve barbecue sauce.
Note: Do not let egg mixture remain at room temperature for longer than one hour (including preparation and service time).