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For the lemon basil granita: Place the cardamom, shallots, chile, salt, sugar and 2 cups water in a pot and bring to a simmer over medium-high heat.
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Cook for 1 minute and remove from the heat.
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Add the basil, lemon zest, cucumber juice and vinegar and stir.
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Cover and let steep for 20 minutes.
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Strain the mixture and place it in the refrigerator to chill.
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Pour into a shallow glass pan and freeze for 4 hours, stirring occasionally, until the liquid becomes slushy.
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Continue to freeze, scraping the top of the granita every 30 minutes to produce fine crystals of shaved ice.
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Freeze until the granita is completely made up of ice crystals.
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For the white pickling marinade: Combine the vinegar, sugar, salt and 1/2 cup water in a saucepan and bring to a simmer, stirring occasionally, until the sugar and salt are dissolved.
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Immediately remove from the heat and set aside.
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For the pickling marinade: Heat 1/4 cup of the olive oil in a saucepan over medium heat.
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Sweat the shallots, garlic, salt and sugar until soft, 2 to 3 minutes.
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Add 1 cup of the white pickling liquid (reserve the remainder for another use) and cook until almost completely reduced and very little liquid remains.
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Cover with the remaining 3 3/4 cups of olive oil and add the thyme and tarragon.
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Immediately remove from the heat and set aside.
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For the avocado coulis: Place the avocado, lime juice, salt and 1/4 cup water in a blender or food processor and puree until smooth.
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Keep chilled until ready to serve.
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For the cobia: Set aside 1 cup of the pickling marinade for the salad and bring the remaining 3 cups to a quick simmer in medium saucepan over medium-high heat.
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Season the cobia with the salt and slip it into the marinade for 30 seconds, then remove the pan from heat.
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Transfer the cobia to a baking dish, pour the marinade over the top and chill in the refrigerator so that the cobia is rare to medium-rare in the center, about 10 minutes.
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The fish will cure slightly.
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If you prefer the fish to be more cooked, leave it in the hot marinade for up to 1 minute.
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For the salad: Remove the cobia from the marinade, pat it dry with paper towels and slice it into thin pieces.
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Mix the cobia with the oranges, avocado, jicama and chile oil to taste, using some of the reserved cup of pickling marinade to dress the salad.
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Season to taste.
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To plate, spread a layer of the avocado coulis on the bottom of 4 wide bowls and top with equal portions of the salad.
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Scrape the granita into 4 portions, each about the size of a golf ball, and top the salads with the the granita.
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Garnish with the lemon basil and jalapeno.
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Serve immediately.
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This recipe was provided by a chef, restaurant or culinary professional and makes a large quantity.
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The Food Network Kitchens have not tested it for home use and therefore cannot make any representation as to the results.