Preheat the oven to 350ºF. Line an 8" x 11" baking pan with parchment paper or aluminum foil.
In a blender or food processor, combine the basil, walnuts, half of the garlic, and optional salt. Blend until the mixture resembles a coarse meal.
Arrange the artichoke hearts in 2 separate mounds in the prepared pan. Top with the tomato and sprinkle with the thyme, remaining garlic, and pepper to taste. Place one salmon fillet on top of each artichoke mound and season with pepper. Spread the basil mixture on the fillets. Drizzle each fillet with 1⁄2 tablespoon of the olive oil.
Bake for 20 to 25 minutes, until the fillets are no longer translucent in the center and the fish flakes when pressed with a fork. Serve immediately.