Wash the vegetables. Finely chop the fennel and onion. Crush the garlic clove with the back of a knife blade. Quarter the tomatoes. Roughly chop the lobster heads. Heat the oil in a saucepan and sweat* the heads. Add the butter and caramelize. Add the fennel, onion, and garlic; sweat for 5 minutes. Add the tomatoes and tomato paste; cook for 3 minutes. Deglaze* with the Cognac and white wine. Reduce* to a thick shiny Jus*, then add the water. Season with salt and a few peppercorns; cook for 30 minutes. Remove from the heat and strain the fumet using a chinois, pressing down on the lobster heads.
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