Snap off tough ends of asparagus. Steam, covered, 2 minutes or until crisp-tender.
Combine mayonnaise and pesto in a bowl, and stir with a whisk. Spread 2 tablespoons pesto mixture onto 1 side of each bread slice. Layer each slice with 8 asparagus spears, 1 ham slice, 2 tomato slices, and 1 cheese slice. Place on a baking sheet; broil 3 minutes or until cheese melts. Sprinkle with pepper.