1Heat coals or gas grill for direct heat. Cut each turkey tenderloin crosswise into 3/4-inch slices. Place half the slices of each tenderloin on one side of each of 4 sheets of heavy-duty aluminum foil, 18x12 inches. Top each with equal amounts of asparagus and carrots.
2Mix remaining ingredients until well blended. Carefully pour one-fourth of sauce over each portion of turkey and vegetables. Fold other half of foil over turkey and vegetables so edges meet. Seal edges, making a tight 1/2-inch fold; fold again. Allow space on sides for circulation and expansion. Repeat folding to seal each side. Place foil packets on cookie sheet to carry to grill.
3Cover and grill packets 4 to 5 inches from medium-high heat 15 to 20 minutes or until turkey is no longer pink in center and vegetables are tender. Place foil packets on plates. To serve, cut a large X across top of packet; fold back foil.