Place meat in slow-cooker with seasoning packet. Add enough water to cover. Cook until tender.
When done, remove from water and let cool 20 minutes on a cutting board covered with foil.
Combine cabbage, cilantro, mayonnaise, sea salt, and adobo sauce in a large bowl. Let chill in refrigerator until ready to assemble the sandwiches.
Slice corned beef into 1/2 inch slices against the grain.
Slice the rolls in half to open them without cutting all the way through. Place cheese slices over the open rolls; toast under a broiler until the cheese has melted.