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1
Chop the parsley very fine.
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2
Smash the garlic, chop it just a little to make grinding easier, and then work it into a paste with a small pinch of salt in a mortar.
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3
Add the parsley and continue to work the mixture in the mortar until smooth.
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4
In a 4-quart pot, bring 2 cups water to a boil, lightly salt it, and add the mussels.
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5
Cover and cook over high heat for 3 to 5 minutes, checking the mussels often and transferring them to a plate as soon as they open.
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6
Discard any that do not open.
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7
Strain the mussel broth through a fine-mesh sieve and reserve it.
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8
Shuck half of the mussels.
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9
Set a large steamer basket over a pot filled with a couple of inches of boiling water, and add the potatoes.
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10
Cover and cook until the potatoes are close to halfway done, 4 minutes.
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11
Meanwhile, drizzle the fish with oil, season it with salt and pepper, and put it on a plate that will fit in the steamer basket, making sure the fillets do not touch each other.
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12
When the potatoes are almost halfway done, add the plate of fish to the steamer basket, and steam for about 6 minutes, until the fish is barely cooked through and the tip of a sharp knife inserted in the thickest part of the fish for 5 seconds comes out warm to the touch.
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13
Transfer the fish and potatoes to a warm platter and cover to keep warm.
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14
In a large, deep saute pan, bring the reserved mussel liquid to a simmer.
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15
Add the parsley mixture and cook for 45 seconds.
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16
Remove from the heat, add the shucked and unshucked mussels, stir to reheat, and swirl in the butter.
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17
Add salt if necessary before spooning the mixture over the fish and potatoes.
