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1
Trim and discard the dark green ends of the leeks, leaving about 2 inches of light green intact.
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2
Cut each leek in half lengthwise, then cut it crosswise into 1/4-inch strips.
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3
Place in a colander, thoroughly rinse, and shake dry.
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4
Place the leeks, broth or stock, wine, vinegar, 1 tablespoon of the butter, and the measured salt in a large frying pan over medium heat.
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5
Season with pepper and bring to a simmer, stirring occasionally.
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6
Nestle the parsley, thyme, and bay leaf into the liquid and leeks.
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7
Reduce the heat to low, cover with a piece of aluminum foil large enough to reach over the pans edges, and cover the foil with a tightfitting lid.
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8
Let braise until tender, about 30 minutes.
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9
About 5 minutes before the leeks are ready, prepare the fish: Pat both sides of the fillets dry with paper towels and season both sides with salt and pepper.
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10
Place the remaining tablespoon of butter and the oil in a large heavy-bottomed frying pan or cast-iron skillet over medium-high heat.
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11
Once the butter melts, swirl the pan to combine the butter and oil.
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12
Add the fillets and cook, undisturbed, until the edges begin to turn opaque and the fish releases from the pan, about 3 minutes.
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13
Using a flat metal spatula, flip the fillets and cook until firm to the touch and opaque in the middle, about 3 to 5 minutes more.
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14
To serve, use a slotted spoon to divide the leeks among 4 shallow bowls.
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15
Place a piece of halibut over the leeks in each bowl, spoon over the desired amount of the leek braising liquid, and sprinkle with the chives.
