Lay a single stalk on its side on a cutting board. Holding onto the tough end, use a vegetable peeler to shave off thin asparagus ribbons from stalk to tip, peeling away from the tough end in your hand. Discard the tough ends once you’re done peeling. Gently pile your ribbons in a large bowl and toss in the greens. Season with salt and pepper.
Step 2In a small bowl, whisk together the olive oil, lemon juice, honey, mustard, salt and pepper. Drizzle over the vegetables. Toss gently and divide the salad amongst 4 plates. Place a fried egg on top of each plate and garnish with fresh lemon zest, dill and sesame seeds.