Cut lemon grass pieces in half lengthwise. Tie lemon grass pieces into a bundle with 100-percent-cotton string. Combine broth, lemon grass bundle, mushroom slices, and pepper in a medium saucepan. Bring mixture just to boiling. Reduce heat; simmer, uncovered, for 10 minutes.
Remove lemongrass bundle. Add cooked chicken and asparagus. Simmer, uncovered, for 3 minutes or until chicken is heated through and asparagus is crisp-tender. Remove from heat. Stir in green onion. Ladle into warm soup bowls. Top with fresh basil leaves, if desired. Makes 4 servings.