Combine the tomatoes, tarragon, and 1 tablespoon of the garlic in a medium-size nonreactive saucepan over medium heat. Season with salt and cayenne. Stir in 3 tablespoons of the vinegar and the wine, and bring to a boil. Reduce the heat to medium-low and simmer until the mixture is dark brown and thick, 20 to 25 minutes. Remove from the heat and stir in the parsley.
Set a stainless steel bowl over a pot of simmering water. Add the egg yolks with the lemon juice and water, and season with salt and cayenne. Whisk until the eggs are pale yellow in color and slightly thick. Remove the bowl from the pot and whisk in the butter, 1 tablespoon at a time, until all the butter is incorporated. Fold the tomato mixture into the egg mixture, set aside, and keep warm.
In a large, heavy pot or an electric fryer, heat the vegetable oil (about 4 inches) to 360?F. Fry the potatoes until golden brown, 3 to 4 minutes. Drain on paper towels. Season with salt and black pepper.
Heat the olive oil in a large sautÈ pan over medium heat. Add the onions, season with salt and cayenne, and cook, stirring, for 2 minutes. Add the remaining 2 teaspoons garlic and the trout. Season with salt and cayenne and cook, stirring, for 1 minute. Add the potatoes, season with salt and cayenne, and cook for 2 to 3 minutes, stirring gently.
Pour cold water into a 10-inch sautÈ pan to a depth of about 2 inches. Bring to a simmer, then reduce the heat so that the surface of the water barely shimmers. Add the remaining teaspoon vinegar. Break the eggs into individual saucers, gently slide them, one at a time, into the water, and with a large spoon, lift the white over the yolk. Repeat once or twice to enclose the yolk completely in the white. Poach until the whites are set and the yolks feel soft when touched gently, 3 to 4 minutes.
When ready to serve, spoon the trout hash into the center of 4 plates. With a slotted spatula, gently lift the eggs out of the water and let them drain a few seconds, season with salt and cayenne, then transfer the eggs to the top of the hash. Drizzle with the sauce and garnish with chives.
Yield: 4 servings