Heat a small skillet over medium heat and add walnuts. Cook, tossing often, until lightly toasted, about 4-5 minutes. Remove from skillet immediately to prevent over-cooking.
· Bring a pot of salted water to boil. Prepare a large bowl of ice water.
· Remove tips from asparagus and place in a pot of boiling water. Cook 1-2 minutes until bright green, strain and plunge into a bowl of ice water.
· Using a vegetable peeler, thinly shave the asparagus stalks and the carrots into thin strips and place in a bowl.
· Thinly slice the radishes and add to bowl with asparagus and carrots.
· Prepare vinaigrette: In a small bowl, mix vinegar, mustard, shallot, salt, and pepper. Slowly whisk in the oil.
· Place arugula or spinach in a separate bowl and toss with a little of the dressing.
· Divide arugula or spinach between 4 plates and top with asparagus, carrot and radish mixture.
· Drizzle a little more dressing over vegetables and top with blanched asparagus tips and toasted walnuts.