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Steam the asparagus until just tender, then rinse in cold water to stop the cooking process. Set aside.
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In a medium bowl, combine the paprika and Old Bay, stirring to mix. Set aside. Coarsely chop the hearts of palm add to the spice mixture in the bowl, tossing gently to coat.
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In a small bowl, combine the mayo, lemon juice, dill, capers, sriracha, and salt and pepper to taste. Mix well, then add the hearts of palm and reserved asparagus and mix gently to combine. If not serving right away, cover and refrigerate until needed.
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When ready to serve, cut the avocados, peel, pit, and cut them in half lengthwise. Cut the avocado halves into lengthwise slices and arrange the slices fanned out on plates lined with lettuce leaves). Mound the hearts of palm mixture on top of the avocado slices. Serve immediately.