Preheat the oven to 350°F. Place the almonds on a baking sheet and toast for 7 minutes, or until golden. Cool for a few minutes, then chop coarsely and set aside.
Whisk together 1 1/3 cups of the oil and the vinegar, orange juice, zest, capers, and anchovies in a small bowl. Season with salt and pepper. Set aside.
Preheat a gas or charcoal grill to medium-high heat. If you are using a charcoal grill, build a fire with coals and let it burn down until the coals are glowing red with a thin coating of white ash. Spread the coals out in a single layer. Brush a grill grate with oil, place the grill grate on the regular grate and preheat for 5 minutes. Brush the salmon fillets with 2 tablespoons of oil. Place the fillets skin side down on the hot grill grate and grill for 3 minutes. Gently turn the fish with a spatula or tongs, and cook for another 4 to 5 minutes on the other side, or until the fish is firm but not hard. To check if the fish is done, insert a knife into the thickest part of a fillet; the center should be slightly translucent. Alternatively, brush the salmon fillets with 2 tablespoons of oil and bake at 400°F for 10 to 12 minutes, or until it pulls apart when pierced with a fork. Remove the skin from the fish and transfer the fillets to serving plates; they will continue to cook as they rest.
Spoon ¼ to 1/3 cup of the sauce over each piece of the grilled (or baked) salmon.
Slice the avocados, if using, into thin slices to serve as garnish. To serve warm and help prevent browning and loss of color, heat the avocado slices with a little oil in a large sauté pan over medium heat until warm, about 1 minute. Place the raw or warmed slices around the salmon and drizzle sauce over the platter. Finally, sprinkle the chopped almonds on top.