Clean morels of any dirt and grit in a large bowl of water. Dry with paper towels.
Trim and discard the stems. Put cleaned and trimmed morels in a large bowl.
Melt the butter and drizzle over the morels. Toss gently to thoroughly coat, sprinkling with sea salt.
Grill mushrooms on KUDU over medium heat until morels are cooked with crispy bits on the edges (about 8 minutes). Serve hot.