Rub the steak on both sides with a mixture of the garlic, pepper, and salt, pressing in the mixture with your fingers. Place the asparagus in a shallow dish and drizzle with the oil.
For sauce, in a medium skillet stir together the broth and wine. Cook over high heat for 4 to 5 minutes or until mixture is reduced to 1/4 cup. Whisk in mustard; keep warm.
Preheat grill on high setting. Place steak on the grill rack, close lid. Grill until steak is desired doneness. (3 to 4 minutes for medium rare or 5 to 7 minutes for medium, turning steak once.) Add asparagus to grill for the last 4 to 5 minutes of grilling. Cook asparagus until crisp-tender.*
Spoon sauce on serving plate. Cut steak in half crosswise. Serve steak halves atop sauce with asparagus on top.
*Note: The asparagus cooking time will vary with the size of asparagus. Also, if there is no room on the grill, the asparagus can be grilled after the steak.