For the olive butter
1 garlic clove, crushed
1 small shallot, peeled
About 18 oil-cured olives, pitted
1 tablespoon chopped fresh Italian parsley
1/2 cup (1 stick) unsalted butter, at room temperature
2 teaspoons Dijon mustard
Freshly ground black pepper
Kosher salt, as needed
For the salmon
6 ounces orzo, acini di pepe, or other small seed-shaped pasta
1 medium (about 2 pounds) wild king salmon fillet, scaled and cut into 4 pieces of equal weight
Ground black pepper
Small Italian parsley sprigs, for garnish
1/4 cup small olives, such as niçoise or Umbria, for garnish
To make the olive butter: Put the garlic, shallot, olives, and parsley in a food processor and pulse several times until the mixture is evenly chopped. Add the butter and mustard and pulse until the mixture is smooth. Season with black pepper, taste and, if the flavors haven’t quite come together, add a pinch or two of kosher salt and pulse again briefly.
Transfer the butter to a sheet of parchment paper and shape into a log about 1 1/4 inches in diameter. Wrap tightly in the parchment and then again in plastic wrap and refrigerate for up to 5 days. To use, unwrap and slice into 1/4-inch coins. (Makes about 1/2 cup.)
To make the salmon: Heat an outdoor or stove-top grill to medium heat while you fill a medium saucepan half full with water, add a tablespoon of kosher salt and bring to a boil. When the water boils, add the pasta, stir, and cook according to the package directions until just tender. Drain thoroughly (do not rinse), transfer to a warm bowl, and toss with 2 tablespoons of the olive butter. Cover with a tea towel to keep warm.
Meanwhile, season the salmon fillets with salt and pepper. Grill skin side up for 8 minutes, rotating once to mark. Turn the salmon over and grill (2 to 3 minutes for a 1-inch fillet, longer if the fish is thicker) until it is just cooked through. Just before removing the salmon from the grill, top each piece with a round of olive butter.
To serve, divide the pasta among 4 warm plates and set a salmon fillet on top, skin side down. Top each piece of salmon with another thin round of olive butter, garnish with olives and parsley, and serve immediately with Golden Roasted Beets with Olives.