Place the asparagus and 1/3 cup water in a microwave-safe bowl. Cook in the microwave on High 1 minute, or just until tender. Rinse under cold water, and blot dry with paper towels.
Spread 1 side of 6 bread slices with 1/4 teaspoon butter and about 1 tablespoon mayonnaise each. Layer with asparagus, and sprinkle with Parmesan cheese. Place lettuce over the asparagus, season with pepper, and top with remaining 6 bread slices to form 6 sandwiches. Slice on a diagonal; this is a sandwich that exudes spring !
