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Clean and trim the leeks and cut into rings. Set some rings aside for garnish, if you like
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Cut the bacon into small pieces and place in a skillet.
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Add the chopped leeks and fry for about 5 minutes.
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Melt the butter in a large saucepan. Add the flour to the butter and stir to combine.
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Slowly add the cream and then the vegetable broth while stirring constantly.
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Bring the mixture to a boil. Turn the heat down to low and simmer for 10 minutes.
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Add the leek and bacon mixture to the hot liquid (reserve some of the bacon for additional garnish if you wish) and simmer for an additional 10 minutes.
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Use a hand blender to puree the mixture. Alternatively, transfer the mixture to a food processor or blender to puree and then transfer back to the pot.
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Stir in the mustard and season with the salt and freshly ground pepper to taste.
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Remove from heat, divide among 4 bowls, garnish and serve.