Preheat the oven to 400°F.
In a small bowl, combine the butter, garlic, lemon zest, mustard, parsley, salt, and pepper to make the compound butter. Put aside.
Place the salmon fillets in an 8-by-8-inch baking dish and drizzle with olive oil.
Allow to stand for 20 minutes at room temperature after seasoning with salt and pepper.
Cook for 10 to 12 minutes, or until an instant-read thermometer reads 125°F. When flaked with a fork, a softer, slightly translucent pink should appear toward the centre of the flesh.
Remove the salmon from the oven and, while still hot, spread 2 tablespoons of the compound butter over the top.
Sprinkle with the parsley and serve hot.