Preheat the broiler.
Place 2 avocado halves in a large bowl and mash lightly with a fork.
Add mayonnaise and lemon juice; mix until smooth.
Stir in crabmeat, 3 tablespoons cilantro, chives, serrano pepper, capers, and pepper.
Spoon the mixture evenly into the remaining avocado halves.
Arrange on a baking pan.
Sprinkle with shredded cheese and paprika.
Broil 4–5 inches from heat for 3–5 minutes until cheese is melted and bubbly.
Remove and sprinkle with remaining cilantro.
Serve immediately with lemon wedges.