Place crackers in a blender or food processor; process until finely ground. Place bread in blender or food processor; process until finely ground.
Combine crabmeat, mayonnaise, cracker crumbs, breadcrumbs, egg white, and next 4 ingredients in a large bowl. Cover and chill 8 hours.
Shape crab mixture into 6 (4-inch) patties. Cook crab cakes, in batches, in hot oil and melted butter in a large skillet over medium-high heat 4 minutes on each side or until golden.
Place avocado slices and poached eggs on crab cakes, and top with Caribbean Hollandaise Sauce and pepper. Garnish, if desired.