You'll have more than enough mint butter for the tender asparagus. Try melting a bit over lamb chops or fresh peas -- classic partners for the herb.
Make the butter: Melt butter with mint, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a small saucepan over medium heat until just bubbling around edges.
Make the asparagus: Cook asparagus in a pot of salted boiling water until bright green and tender, about 3 minutes. Drain.
Drizzle a few tablespoons mint butter over asparagus, and toss gently to coat. Garnish with mint leaves.
Mint butter can be refrigerated in an airtight container for up to 1 week.