Halve leeks lengthwise and thinly slice crosswise. In a large bowl of cold, water wash leeks well and lift from water into a large sieve to drain. In a 6-quart heavy soup pot, cook leeks in butter over moderately low heat, stirring occasionally, until some begin to turn golden, about 40 minutes. Stir in sugar and cook, stirring occasionally, 10 minutes. Stir in vermouth and cook, stirring occasionally, until liquid is evaporated and most leeks are golden, 10 to 15 minutes. Deglaze pot with 1/2 cup broth and cook, stirring occasionally, 10 minutes more, until liquid is evaporated and leeks are deep golden. Add remaining 3 cups broth and bring soup just to a boil. Season soup with salt and pepper.;
Diagonally cut 8 (1/2-inch thick) slices from the bread, reserving remainder for another use. On a baking sheet toast 1 side of bread slices under broiler about 4 inches from heat and leave broiler on. Using a cheese plane, thinly slice raclette. Turn the bread over and spread 1/2 teaspoon mustard on untoasted side of each slice. Top toasts with cheese and broil until cheese is just melted, about 2 minutes.
Yield: 8 toasts