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1
In a skillet cook 3 cups of the onions in 1/2 cup water over moderate heat for 15 to 20 minutes, or until they are very soft.
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2
Add the vinegar and cook the mixture for 2 minutes, or until the liquid is evaporated.
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3
Add the broth and simmer, stirring for 30 minutes.
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4
Strain the liquid through a sieve into a bowl, reserving it, and in a food processor puree the onions with 1/4 cup of the reserved liquid.
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5
In a saucepan, boil remaining reserved liquid until reduced to about 1 cup.
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6
Stir the onion puree into the reduced liquid, stir in the cream, and keep the sauce warm, covered, over very low heat.
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7
Toss the remaining 2 cups onions with the flour, shake off the excess, reserving it.
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8
In a deep fryer, heat the peanut oil to 375F and fry the onions, a few at a time, for 1 to 1 1/2 minutes.
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9
Transfer the onions with a slotted spoon to paper towels to drain and chop them into 1/4-inch pieces.
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10
In an ovenproof skillet heat the olive oil over moderately high heat until hot but not smoking and cook the salmon, skin side up and seasoned with salt and pepper, for 1 1/2 minutes.
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11
Turn the fillets carefully with a spatula and cook them for 2 minutes more.
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12
Dip the tops of the fillets carefully into the reserved flour, coat them with the egg, and top them with the fried onions.
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13
Return the fillets to the skillet, spoon any remaining fried onions on top of the fillets, and bake the fillets, covered loosely with foil, in the middle of a preheated 350F oven for 4 to 5 minutes, or until just cooked through.
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14
Divide the sauce among 4 heated plates, transfer the salmon with a spatula to the plates and spoon the caviar decoratively onto it.
