Heat the extra-virgin olive oil, 3 turns of the pan, in a skillet over medium to medium-high heat. Add onions and cook until caramel colored, stirring occasionally.
Pour 1-inch of water into a skillet and bring to boil. Add salt and asparagus and cook 3 minutes, drain.
Stir in thyme, mustard, balsamic vinegar and pepper into onions and toss with asparagus to coat.