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1
Remove the skin from the salmon fillet.
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2
Set the skin aside.
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3
Cut the skinless fillet into four pieces of equal size.
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4
Set aside.
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5
Melt one tablespoon of the butter in a saucepan and add the shallots, carrots and garlic.
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6
Cook briefly, stirring.
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7
Add the thyme sprigs, bay leaf and reserved salmon skin.
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8
Cook, stirring, about three minutes and sprinkle with arrowroot.
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9
Stir to blend and add the wine.
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10
Bring to the simmer and cook over low heat about 15 minutes.
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11
Line a bowl with a sieve and pour the sauce into the sieve.
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12
Press with a spatula or the back of a large spoon to extract as much liquid as possible from the solids.
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13
There should be about three-quarters of a cup.
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14
Discard the solids.
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15
Heat one tablespoon of butter in a skillet, preferably of the nonstick variety, large enough to hold the salmon pieces in one layer.
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16
Sprinkle the salmon pieces with salt and pepper and add them to the skillet.
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17
Cook two to three minutes (the cooking time will depend on the thickness of the fish pieces) and turn.
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18
Cook two to three minutes on the second side.
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19
Sprinkle with the marc de bourgogne and pour the strained red-wine sauce over the fish.
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20
Turn the pieces in the sauce and transfer the pieces to a warm platter.
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21
Swirl the remaining two tablespoons of butter into the sauce and pour it over the fish.