Bring a medium pot of water to a boil, add shrimp, and poach until curled and pink and just barely opaque in center (cut one to check), 2 1/2 to 3 minutes. Drain and pour into a bowl of ice water. When cool, drain again and chop into 1/2-in. dice. Chill until using.
Make ginger sambal: Purée sambal ingredients in a blender or food processor (add water as needed to make it pourable), then chill until using.
Make vinaigrette: In a small bowl, whisk together lime juice and oil.
Just before serving, put shrimp, pineapple, jicama, onion, chiles, cilantro, and mint in a large bowl. Toss gently with lime vinaigrette and add salt to taste.
Divide shrimp cocktail among 8 to 10 small bowls or glasses and drizzle sparingly with ginger sambal. Serve with extra sambal on the side.
*Jicama, a juicy, crunchy, slightly sweet tuber, is best when small (bigger ones tend to be dry and starchy). Buy them from a place that has high turnover, like a Mexican market or farmers’ market. Find sambal oelek at well-stocked grocery stores, Asian markets, and online.