Snap off tough ends of asparagus. Cook in boiling water to cover 3 minutes or until crisp-tender; drain. Plunge into ice water to stop the cooking process; drain and chill.
Stir together butter and garlic.
Spread butter mixture evenly over bottom halves of bread. Spread mayonnaise evenly over top halves of bread. Layer bottom halves evenly with ham slices, asparagus, and cheese; place on a baking sheet.
Broil 2 inches from heat 1 minute or just until cheese melts. Top evenly with lettuce, tomato, and top half of bread.
* 6 ounces thinly sliced Brie with rind removed may be substituted for Swiss