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1
Preheat the oven to at least 450 degrees.
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2
Place a cast-iron or other ovenproof skillet inside.
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3
Put half the butter in a small saucepan, and turn the heat to medium-high.
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4
Add carrot and celery, and stir; a minute later, add onion.
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5
Cook, stirring occasionally, until vegetables brown, less than 10 minutes.
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6
Be careful not to let them burn.
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7
Stir in tomato paste if you like, then broth.
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8
Bring to a boil, adjust heat and let mixture simmer about 10 minutes.
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9
Strain mixture, pressing on vegetables to extract their liquid, and return to medium-high heat.
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10
Bring to a boil; let boil until less than half a cup of thick liquid remains.
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11
Meanwhile, season fish with salt and pepper.
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12
Carefully remove hot pan from oven, and add oil; swirl to coat bottom.
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13
Add fish, and roast 5 minutes.
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14
Remove from oven, and carefully pour liquid accumulated around fish into simmering sauce; turn fish over, and return to oven for 5 minutes while bringing sauce to a boil.
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15
Reduce sauce until it is thick and syrupy and measures about 1/2 cup.
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16
When a thin-bladed knife inserted into thickest part of fish meets little resistance, remove it from oven.
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17
Add remaining butter to sauce, and spoon over fish to serve.
