Preheat oven to 425 degrees F. Line a baking sheet with parchment paper. Spread the lime juice on a wide plate. Quarter the avocado lengthwise, pull it apart, and discard the pit. Remove the peel from the avocado. Cut each quarter piece of avocado, lengthwise, into three slices. Set the avocado on the plate and coat with the lime juice.
Spread one side of each bread slice with mayonnaise and set on the baking sheet. Divide and arrange some arugula or spinach on each bread slice. Set 2 slices of tomato, and 3 slices of avocado, on top of each bread slice. Divide and top each melt with the cheese.
Bake 10 minutes, or until the cheese is melted and the bread is lightly toasted. Sprinkle each melt with some cilantro and serve.
Recipe Options: In you don't care for the spicy tasting, Jalapeno-flavoured cheese, top the melts with plain Monterey Jack cheese. If you don't care for cilantro, sprinkle the melts with sliced green onion instead. If you're a meat eater, top each melt with some sliced or shredded cooked chicken breast before topping with the cheese and baking.