Mix together ingredients for the nuoc cham sauce in a small bowl and set aside.
Mix together all ingredients for Hoisin dipping sauce EXCEPT chopped peanuts in a small saucepan.
Bring mixture to a boil; then reduce heat and simmer for five minutes.
Cool Hoisin dipping sauce to room temperature, garnish with chopped peanuts, and set aside.
Het oil in a large skillet, add asparagus and cook for one minute.
Add water and cook, covered, for three minutes more; remove from heat.
Note: crab is meant to be chilled and asparagus is meant to be cooled down to room temperature when building rolls.
Fill a large bowl with warm water (deep enough to submerge a rice paper).
Dip one rice paper at a time while building soft rolls, just till it becomes pliable; remove from water and blot on paper toweling.
To build roll, on softened rice paper, place a lettuce leaf with margins on all sides (except top is ok).
Top lettuce with one ounce of crab, one piece of asparagus, a couple of pinches of alfalfa sprouts and shredded carrots, a fresh basil leaf, and a couple of cilantro sprigs.
Fold bottom edge of rice paper up over filling, then wrap right side over filling and roll up tightly into a bundle.
Place on serving platter covered with a damp paper towel while preparing remaining rolls.
Serve at once with dipping sauces and hot chile paste (sambal oelek), if desired.