In a large, high-sided skillet, heat 2 tablespoons of the peanut oil until simmering. Add half of the spinach and cook over moderately high heat, tossing, until slightly wilted. Add the remaining spinach and cook, tossing, until wilted. Season with salt and transfer to a colander to drain.
Add the remaining 1 tablespoon of peanut oil to the skillet and heat until shimmering. Add the carrots and onion and stir-fry over moderately high heat until slightly softened, about 1 minute. Stir in the coconut milk, green curry paste and sugar and simmer over moderate heat until the carrots are tender, about 3 minutes. Remove from the heat and add the lime juice and fish sauce; season with white pepper. Transfer the curry sauce to a bowl.
In a clean large skillet, heat 3 tablespoons of the vegetable oil until shimmering. Season the scallops with salt and add half of them to the skillet. Cook over moderately high heat, turning once, until well browned and just white throughout, about 4 minutes. Transfer to a plate. Wipe out the skillet. Repeat with the remaining 3 tablespoons of vegetable oil and scallops.
Mound the spinach on 6 plates. Top with the curry sauce and scallops. Garnish with the chopped peanuts and lime zest and serve immediately.