Make the sauce: In a large (12-inch) skillet over medium heat, heat the oil until shimmering. Add the onion and cook, stirring occasionally, until softened but not browned, about 3 minutes. Add the garlic and ginger and cook until aromatic, about 30 seconds. Stir in the curry powder, paprika, salt and black pepper to coat the onions and warm the spices, about 30 seconds more.

Add the tomatoes and coconut milk, and bring to a boil. Reduce the heat to medium-low and simmer, stirring occasionally to prevent scorching on the bottom, until the sauce thickens slightly and the flavors meld, about 10 minutes. Taste, and season with cayenne pepper, if desired. Remove from the heat and let cool in the pan for about 15 minutes, then transfer to a blender and blend until smooth. (Alternatively, transfer the sauce to a deep container and use an immersion blender to process until smooth.) You should have about 2 cups; use right away or refrigerate until needed.

Finish the dish: In a large (12-inch), high-sided skillet over medium-high heat, heat the oil until shimmering. Working in batches, add the shrimp and cook until it turns pink and is lightly browned and nearly cooked through, 1 to 2 minutes per side. Transfer the browned shrimp to a plate and repeat with the remaining shrimp, adding more oil to the pan, if it looks dry.

Return the shrimp to the pan, then add the sauce and reduce the heat to medium-low. Cook at a gentle simmer until the sauce is warmed through and the shrimp are cooked through and opaque, 2 to 3 minutes. Stir in the spinach or kale, adding in batches if needed, and cook until just wilted, 30 seconds to 1 minute.

Divide the rice among individual bowls, top with the shrimp mixture and serve hot.