With skin side down, drizzle oil and lemon over fish. Salt and pepper to taste, spread zest, herbs and spices over fish to taste. Let set at room temperature 10 to 15 minutes; cover and refrigerate if longer.
Fire up grill or oven. Place filets in a grill basket or sheet or on aluminum foil; set on preheated grill or in 375-400 degrees F oven. Cook for about 6 minutes per inch of thickness of the salmon.
Remove from grill/oven and cover; allow fish to rest for a few minutes. Drizzle filets with aioli, sprinkle with chopped parsley and serve.