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Thaw fish, if frozen. Rinse fish; pat dry with paper towels. Snap off and discard woody bases from asparagus. Brush both sides of fish and asparagus lightly with olive oil. Sprinkle fish and asparagus with salt and pepper.
For a charcoal grill, place fish on the greased rack of an uncovered grill directly over medium coals. Place asparagus on grill rack next to salmon. Grill for 8 to 12 minutes or until fish begins to flake when tested with a fork and asparagus is tender, turning fish once halfway through grilling, and turning asparagus occasionally. (For a gas grill, preheat grill. Reduce heat to medium. Place fish and asparagus on a greased grill rack over heat. Cover and grill as above.)
Meanwhile, for garden mayonnaise, in a small bowl stir together celery, mayonnaise, green onions, lemon juice, and tarragon. Chill until serving time.
To serve, arrange fish and asparagus on 4 dinner plates. Top fish with garden mayonnaise. If desired, serve with lemon wedges.