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1
In a small, deep saucepan, pour in enough oil to measure 1 inch deep; heat over medium-high heat until the oil registers 350 degrees F on a deep-fat frying thermometer.
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2
Set a small strainer over a large glass measuring cup. Line a bowl with paper towels.
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3
When the oil is hot, add the leeks and cook until lightly browned and crisp, about 1 minute, stirring constantly. Immediately remove the pan from the heat and pour the leeks into the strainer. Transfer to paper towels to drain. Strain the oil and reserve for other purposes.
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4
In a medium-size saucepan, melt 2 tablespoons of the butter over medium heat. Add 2 cups of the onions, 1 cup of the leeks, and shallots and saute until soft and golden brown, about 8 minutes. Stir and scrape the pan often to prevent burning.
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5
Meanwhile, in a small skillet, heat the remaining 1/2 tablespoon of butter over medium heat. Add the remaining cup of onion and saute until soft and rich golden brown, 7 to 9 minutes, stirring often. Watch that they don't burn. Set aside.
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6
Pour the sherry into the saucepan with the leeks and shallots and bring to a boil over high heat, stirring up all the browned bits. Scrape the mixture into the jar of an electric blender or food processor, add the tarragon, and puree until smooth. Return the mixture to the saucepan, add the stock and cream; simmer for 5 minutes. Stir in the caramelized onion from the small skillet, season with salt and pepper, and keep warm over medium-low heat.
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7
For the crostini, rub the toasted bread with garlic and brush with oil. Lay the slices on a cookie sheet or on the tray of a toaster oven, sprinkle on the cheese, and broil until the cheese is melted and lightly browned. Ladle the soup into two wide bowls, sprinkle on the leeks, add 2 crostini to each bowl, and serve at once.
