Preheat a gas or charcoal grill or set an oven broiler on high.
Snap the tough bottom section off the asparagus -- usually about 3 inches from the base.
In a small bowl whisk together the olive oil, salt, pepper, lemon juice and zest, mustard, and garlic to make a dressing.
In a large bowl, or on a sheet pan, coat the asparagus with the dressing and marinate for 10-15 minutes, tossing occasionally to redistribute the marinade.
Grill the asparagus on a very hot grill, turning several times, until tender but still crisp-about 3-5 minutes.
Alternately, line up the asparagus in a single layer on a baking sheet and broil, turning several times, until cooked but crisp, also about 3-5 minutes.
Stack the asparagus on a serving platter and sprinkle the cheese over it. Spoon the Romesco over the asparagus and serve hot. It is also perfectly tasty at room temperature.
Serves 4-6 as a side dish.