Prepare the Sweet Cilantro Sauce by whisking all the ingredients together in a small bowl, then set aside.
Spread the shrimp on a plate and chill them in the freezer for 15 minutes to ensure a springy texture for the shrimp cakes. Meanwhile, prepare all your other ingredients. In a food processor or blender, combine the chilled shrimp, red curry paste, egg, fish sauce, sugar, and coconut milk. Process until smooth, about 30 seconds. Transfer the mixture to a mixing bowl and mix in the green beans and basil.
Since different brands of curry pastes have varying salt levels, it's a good idea to make a sample shrimp cake first. Sauté 1 tablespoon of the mixture in a skillet (frying pan). Taste, and if necessary, adjust the seasoning with fish sauce and salt.
Heat a large skillet over medium heat. Use 1 tablespoon of oil to coat the skillet. Then, using a measuring spoon, drop 1 tablespoon of the shrimp mixture into the skillet. With a damp finger, flatten the mixture slightly to about 1/2 inch (1 cm) thick. Repeat this process to make about 10 shrimp patties in the skillet.
Cook the cakes until golden brown on each side and cooked through, about 2 minutes per side. Wipe out the skillet with a paper towel, then make more patties from the remaining mixture and cook them the same way. Serve with a side bowl of sweet chili sauce.