Place the garlic, Italian parsley, and salt in a 12-inch skillet or sauté pan. Add water to a depth of about 2 inches. Bring to a simmer, cover, and let cook for 5 minutes. It should smell very fragrant.
Meanwhile, measure the thickness of the halibut fillets. They will cook for 8 to 10 minutes per inch of thickness.
When the poaching liquid is ready, slip the fillets gently into the pan. Cook for 8 to 10 minutes per inch, adjusting the heat so that the liquid just trembles: it should only bubble a little, and very gently. To test the fish for doneness, make a small slit with a paring knife in the thickest part of the fillet: all but the very center of each piece should be opaque.
When each fillet is ready, use a slotted spatula to transfer it to a serving plate. Garnish the plates with sprigs of Italian parsley and lemon wedges. Serve immediately, allowing each eater to season their fish at the table with olive oil, salt, pepper, and freshly squeezed lemon.
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