To make the mousse, preheat the oven to 350 degrees. Place the fresh salmon in a single layer in a medium ovenproof skillet and sprinkle with salt and pepper. Bring the fish stock to a boil and pour it over the salmon. Over medium high heat, bring the stock to a simmer. Place a buttered sheet of parchment paper over the skillet and transfer it to the oven. Cook for 2 minutes, until the salmon is not quite done. Strain, reserving the salmon and stock in separate bowls.
In a medium saucepan, heat the butter over medium low heat. Add the shallots and the mushrooms and cook for about 3 minutes, or until almost tender. Add the brandy and flame it with a match, standing well away from the pan. Cook over high heat until reduced by half, then add the reserved stock and again reduce by half. Remove from the heat and sprinkle the gelatin over the top. Stir until the gelatin has dissolved, then strain into a food processor and discard the solids. Add the cooked salmon and the Tabasco to the food processor and puree the mixture until smooth. Whip the cream to soft peaks and reserve in the refrigerator. Transfer the salmon mixture to a metal bowl set inside a larger bowl filled with ice water. Stir until the mixture has cooled to room temperature, but not colder. Stir in 1/4 of the whipped cream to loosen the mixture, then fold in the remaining whipped cream gently.
Stop folding as soon as the last trace of white disappears. Pour 1/2 of the mixture into a 10 by 5 by 3inch glass loaf pan and, using half of the smoked salmon, gently lay a layer of smoked salmon over the top, laying the strips crosswise. Fit the avocado slices together into an even layer, taking care not to press down too hard or the mousse underneath will shift. Lay the remaining smoked salmon over the top of the avocado and then scoop the remaining salmon mousse into the pan. Spread the mousse into an even layer and cover with plastic wrap. Chill for at least 6 hours and up to 2 days before serving. To serve, run a thin knife along the inside edge of the pan. Dip the bottom of the pan in hot water for a few seconds and invert onto a rectangular serving platter. Cut the mousse into 3/4inch slices with a very sharp knife transfer carefully to serving plates. Pass the watercress mayonnaise on the side.