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1
Put the oil in a deep skillet and turn the heat to medium-high.
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2
A minute later, add the mushrooms and onion and cook, stirring occasionally, until softened, about 5 minutes.
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3
Add the tomatoes and cook until they break down and release their juices, about 10 minutes.
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4
Stir in the olives, pickles, capers, stock, and salt and pepper and bring to a steady simmer.
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5
Sprinkle the fish with salt and pepper, then gently slide the fillets into the stock and cook just until a thin-bladed knife passes through with little resistance, less than 10 minutes.
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6
Transfer the fish to a warmed serving dish.
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7
Bring the sauce to a boil and reduce slightly.
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8
If you want a thickened sauce, as is traditional, mix the cornstarch with 2 tablespoons cold water and stir into the sauce.
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9
Lower the heat, then simmer until the sauce thickens; taste and adjust the seasoning.
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10
Spoon the sauce over the fish, garnish with parsley, and serve.
