Blanch asparagus in boiling salted water for 1 minute, then transfer to ice water. Drain, dry, and combine with thawed peas.
Make the dressing by pulsing basil, garlic, lemon juice and zest, vinegar, olive oil, and salt in a food processor.
Toss half the dressing with asparagus and peas, and season with salt and pepper.
Layer salad greens on a platter, top with dressed asparagus mixture, radishes, feta, avocado, pistachios, and chickpeas.
Garnish with fresh herbs, drizzle with remaining dressing, and season with salt and pepper before serving.
