Make the dressing: Pulse the parsley, tarragon, lemon juice and mustard in a mini food processor to make a coarse paste. Add the buttermilk, mayonnaise and olive oil; pulse until smooth. Season with salt and pepper. Refrigerate until ready to use.
Make the salad: Prepare a large bowl of salted ice water. Toast the almonds in a small dry skillet over low heat, about 4 minutes; transfer to a plate and let cool. Bring a large pot of salted water to a boil. Add the asparagus and cook until just tender, 4 to 5 minutes. Drain and transfer to the ice water; let cool. Drain again and pat dry; transfer to a large bowl.
Add the lettuce, watercress, radishes, chicken, goat cheese, parsley and half of the toasted almonds to the bowl. Drizzle with about half of the dressing and season with salt and pepper; toss. Sprinkle with the remaining toasted almonds and serve with the remaining dressing.