Bring a medium saucepan of salted water to a boil. Add the asparagus and cook until crisp-tender, about 2 minutes. Drain and transfer to a bowl of ice water to cool, then drain and pat dry.
Meanwhile, make the dressing: Combine the mayonnaise, sour cream, fennel fronds, parsley, tarragon, lemon juice, anchovies, 1/2 teaspoon salt and a few grinds of pepper in a mini food processor. Process until smooth. Refrigerate until ready to serve.
Combine the asparagus, sliced fennel, Boston lettuce, mixed greens, peas, celery and pistachios in a large bowl. Just before serving, drizzle with the dressing, season with salt and pepper and toss.