In a spice mill finely crush the fennel seed. Pour the crushed seed into a food processor along with ½ cup packed spinach leaves and the remaining butter ingredients. Whirl until the spinach and scallions are finely chopped and the butter is well blended, scraping down the sides of the bowl often.
Prepare the grill for direct cooking over medium heat (350° to 450°F).
Season the fillets on both sides with the salt and pepper and arrange them on a 12-by-7-inch sheet pan lined with aluminum foil. Spread 2 to 3 tablespoons of the butter over the top of each fillet. Reserve any butter not used for cooking the remaining spinach.
Brush the cooking grates clean. Cook the fillets on the pan over direct medium heat, with the lid closed, until cooked to your desired doneness, 8 to 12 minutes for medium rare (do not turn). Transfer the pan with the fillets to a heatproof surface. Remove the fillets from the pan and reserve the buttery juices. Keep the fillets warm while preparing the spinach.
Add any reserved butter and the remaining spinach to the sheet pan. Use tongs to coat the spinach with the butter. Place the pan over direct medium heat, close the lid, and cook until the spinach is wilted, 2 to 3 minutes, turning occasionally. Remove from the grill.
To serve, spoon rice onto individual plates. Top with spinach and a salmon fillet.
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