Place all the vinaigrette ingredients except oil in a medium bowl and whisk to combine. Slowly drizzle in oil, whisking continuously, until completely incorporated. Taste and season with additional salt and pepper. Gently stir in the peas.
Arrange the arugula leaves in the center of 4 salad plates. Sprinkle the asparagus and radishes over the plates dividing them equally. Top with the lemon dill vinaigrette.