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1
Preheat the oven to 450F.
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2
Put the sugar in a heavy saucepan, preferably nonstick and with rounded sides, and turn the heat to medium.
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3
Cook, without stirring (just shake the pan occasionally to redistribute the sugar) until the sugar liquefies and begins to turn brown, about 10 minutes.
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4
Turn off the heat and carefully add the wine.
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5
Turn the heat to high and cook, stirring, until the caramel dissolves again.
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6
Then add the rosemary sprig and reduce over high heat, stirring occasionally, until the mixture is syrupy and reduced to just over 1/2 cup, 10 to 15 minutes.
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7
Heat a nonstick ovenproof skillet over high heat until it begins to smoke.
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8
Season the salmon on both sides with salt and pepper, then put it in the pan; immediately put the pan in the oven.
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9
Cook for 3 minutes, then turn the salmon and cook for another 3 minutes.
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10
Check to see that the salmon is medium-rare or thereabouts (it should be) and remove it and keep it warm, or cook for another minute or two if you like.
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11
When the sauce is reduced, stir in the balsamic vinegar and butter and turn the heat to medium-low.
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12
Cook until the butter melts, add some salt and pepper, and remove the rosemary sprig.
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13
Taste and adjust the seasoning, then serve over the fish, garnished with the chopped rosemary.