Peel and trim the asparagus stalks. Cut about an inch of the tips from the spears and then thinly slice the remaining stalk. Bring a small pot of salted water to a boil. Drop the asparagus into the water and cook until just crisp-tender, about 1 minute. Drain and refresh under cold running water. Set aside.
In a medium bowl, whisk together the garlic, shallot, mustard, lemon zest and juice, salt and pepper to taste. Gradually whisk in the oil to make a creamy dressing.
In a large bowl, combine the rice, nuts, carrots, celery, asparagus, dill, and mint. Toss with about 1/3 cup dressing. Serve as is or toss the lettuce with some of the dressing. To serve place the lettuce on a serving platter or individual plates and spoon the salad into the center of the leaves. Pass any remaining dressing at the table.
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