Preheat the oven to 475 degrees. Line a baking sheet with foil. Place one of the oven racks close-ish to the top, about 6 inches or so.
Cook rice according to package instructions.
Mix the spices and the olive oil to make a paste. Place the salmon skin side down on the baking sheet. Rub the paste liberally over the top part of the salmon. Bake for 6-12 minutes (depends on salmon thickness and desired doneness – I usually opt for 8-10 minutes). See notes and FAQs for potential broiling issues and alternative methods.
Heat the olive oil over medium heat. Add garlic, ginger, and lemongrass; sauté for 5 minutes. Add brown sugar and curry paste; sauté for 3 minutes. Add coconut milk. Season with fish sauce, lime juice, and lime zest to taste. Add spinach; stir into the sauce until wilted.
Place salmon over rice. Cover with sauce, lime juice, and fresh herbs.
