SPREAD walnuts on a baking sheet. Bake 5-10 minutes until lightly toasted, stirring once or twice. Cool.
While walnuts are toasting, rinse asparagus and snap tough ends off just where the spear yields to bending. Place spears in a wide skillet. Add cold water to nearly cover. Bring to a boil over high heat. Simmer uncovered 3-5 minutes, turning several times until asparagus is just barely tender.
Rinse parsley and pat dry between sheets of paper towel. Finely chop parsley and place in a small bowl. Remove yellow part of lemon zest with a vegetable peeler; finely mince with a sharp knife. (Or use a grater, but I like the coarser bits of zest).
Add zest to parsley. Stir in cooled walnuts, garlic, salt, and pepper to taste. Arrange asparagus on four salad plates and top with gremolata. Extra gremolata will keep refrigerated 2-3 days. Stir into scrambled eggs, or over other vegetables.