Bring a pot of water to a boil. Gently add the eggs and simmer for 4-6 minutes for softly set yolks. Remove and transfer to an ice bath to cool. Once cooled, peel and set aside.
In the same pot of boiling water, add the asparagus pieces and cook for about 5 minutes until tender-crisp.
Add the peas and cook for an additional 1-2 minutes. Immediately drain and transfer to an ice bath to stop the cooking process. Drain and set aside.
In a small bowl, whisk together the olive oil, lemon juice, and Dijon mustard until combined.
In a large bowl, combine the spinach, arugula, blanched asparagus, peas, radishes, and red onion. Drizzle the dressing over the salad and toss gently to combine.
Divide the salad among serving plates. Halve the soft-boiled eggs and place on top of each salad serving.
Garnish with fresh herbs (chives or parsley) if desired and serve with lemon wedges on the side.