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In a large, deep, straight-sided skillet or heavy pot, combine carrots, celery, onion, lemon, 1 1/2 teaspoons salt, and 6 cups water. Bring to a boil; reduce to a simmer, cover, and cook 8 minutes.
Season salmon with salt and gently lower into simmering liquid (liquid should just cover fish). Reduce to a very gentle simmer.
Cover and cook until salmon is opaque throughout, about 5 minutes (longer for thicker fillets).
Using a wide slotted spatula, remove salmon from liquid.
2 carrots, cut into 1-inch pieces
1 celery stalk, cut into 1-inch pieces
1 small onion, peeled and halved
½ lemon, thinly sliced
Coarse salt
4 skinless salmon fillets (6 ounces each and about 1 inch thick)