Break off the woody parts of the stem so that only about the top 3 inches or so of the stalk remain.
Place the asparagus in a microwavable bowl with just enough water to cover. Place a towel over the top of the bowl. Microwave on 50 percent power until tender (2 minutes). Drain.
Open the package of crescent rolls and spread out the crescent roll dough sheets evenly on a large baking sheet. Roll out each sheet as much as possible. Coat the dough sheet with an even layer of Dijon mustard.
Wrap 1-2 asparagus stalks in 1-2 slices of ham. Place at the wide end of the crescent dough and roll up in the dough. Repeat for each crescent roll.
Bake until slightly golden brown (about 10-12 minutes). Remove from the oven, let cool slightly, and serve warm.