A frozen granita made with honeydew melon, ginger, and sharp Japanese wasabi is an extraordinary accompaniment to chilled shrimp cocktail.
In a small saucepan, simmer sugar and 1 3/4 cups water until sugar dissolves, about 3 minutes. Stir in wasabi and let cool.
In a food processor, puree melon. Measure 2 1/4 cups; discard remainder. Process melon and ginger until smooth, 1 to 2 minutes. Mix in cooled sugar syrup.
Pour into a 9-by-13-inch glass or metal baking dish. Freeze until ice crystals form around the edge, about 45 minutes. Using a fork, gently stir crystals into middle of dish, breaking up clumps. Repeat often until totally set and granular, freezing about 30 minutes each time; this will take about 2 hours.
Peel and devein shrimp, leaving tails on and reserving shells. In a saucepan, bring shells, cilantro, sake, 1 cup water, and salt to a boil. Reduce heat and simmer, skimming scum from surface, until flavorful, about 30 minutes. Pour through a cheesecloth-lined strainer into a skillet, pressing solids to extract liquid. Over high heat, bring liquid to a boil, then reduce heat so liquid simmers. Poach shrimp, adjusting heat to maintain a bare simmer, until pink and cooked through, about 3 to 5 minutes.
Transfer shrimp to a small baking dish. Cover with cooking liquid, let cool, and chill.
Sprinkle cucumber and pickled ginger over granita and fold in using a fork. Spoon into glasses; sprinkle with shiso. Place shrimp over glasses and serve immediately.