Preheat a grill to medium high; oil the grates. Bring a medium pot of water to a boil. Add the noodles and cook as the label directs. Drain and rinse under cold water. Toss the shrimp with 1 tablespoon curry paste and the vegetable oil. Let sit at room temperature, about 15 minutes.
Meanwhile, whisk the remaining 1 tablespoon curry paste, the peanut butter, vinegar, ginger brine, 2 tablespoons water and a pinch of salt in a large bowl until smooth and thick. Add the cucumber, bell pepper, carrot, most of the cilantro, the ginger and a generous pinch of salt; toss well until the sauce loosens. Cut the noodles into shorter pieces with kitchen shears and add to the vegetables; season with salt and toss well.
Grill the shrimp until just cooked through, 2 to 3 minutes per side. Serve on top of the noodle mixture. Top with the remaining cilantro.