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1
Melt the butter in a large saucepan or stockpot over medium-high heat.
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2
Add the onion and cook, stirring occasionally, until softened and translucent, about 5 minutes.
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3
Raise the heat to high and add the fish bones and heads; cook, stirring occasionally, for another 5 minutes or so.
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4
Add 6 cups water, bring to a boil, then reduce the heat so the mixture bubbles a bit and simmer for about 30 minutes, skimming any foam from the surface.
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5
Strain the mixture.
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6
Meanwhile, heat the 3 tablespoons olive oil in a large saucepan over medium-high heat and add the leeks; cook, stirring occasionally, until softened and browned lightly, about 5 minutes.
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7
Stir in the chard; add 1 cup of the fish stock, then cover and cook for another 5 minutes.
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8
Add about half of the remaining stock and bring to a boil; reduce the heat so that the mixture barely simmers, then add the fish.
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9
Poach until just cooked through, 10 minutes (the fish is done when easily pierced with a thin-bladed knife; try not to overcook).
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10
Whisk 1/2 cup aioli into the remaining stock, then gently stir the mixture into the soup.
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11
Season with salt and pepper, garnish with the herb, and serve, passing more aioli at the table.
