How to Make It
In a small bowl, mix the fish sauce with the rice vinegar, lime juice, sugar and garlic, making sure to dissolve the sugar.
In a small saucepan of boiling water, cook the beans until bright green, about 2 minutes. Drain and pat dry with paper towels.
In a food processor, combine the shrimp with the coconut milk, cilantro, lemongrass, chile, fish sauce and salt and pulse to a chunky consistency. Scrape the mixture into a bowl and stir in the green beans. Form into sixteen 1/4-cup patties.
In a large, nonstick skillet, heat the vegetable oil. Add the shrimp cakes and cook over moderately high heat until browned on the bottom, about 2 minutes. Flip and cook over moderate heat until the cakes are browned on the other side and just cooked through, about 3 minutes.
Arrange the mango slices on plates. Set the shrimp cakes on top and sprinkle with the cucumber, peanuts, cilantro and mint. Drizzle the dressing over the shrimp cakes and serve.