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. Cook for 1 minute and remove from the heat. Add the basil, lemon zest, cucumber juice and vinegar and stir. Cover and let steep for 20 minutes.
Strain the mixture and place it in the refrigerator to chill. Pour into a shallow glass pan and freeze for 4 hours, stirring occasionally, until the liquid becomes slushy. Continue to freeze, scraping the top of the granita every 30 minutes to produce fine crystals of shaved ice. Freeze until the granita is completely made up of ice crystals.
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. Immediately remove from the heat and set aside.
For the pickling marinade: Heat 1/4 cup of the olive oil in a saucepan over medium heat. Sweat the shallots, garlic, salt and sugar until soft, 2 to 3 minutes. 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. Cover with the remaining 3 3/4 cups of olive oil and add the thyme and tarragon. Immediately remove from the heat and set aside.
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. Keep chilled until ready to serve.
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.
Season the cobia with the salt and slip it into the marinade for 30 seconds, then remove the pan from heat. 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. The fish will cure slightly. If you prefer the fish to be more cooked, leave it in the hot marinade for up to 1 minute.
For the salad: Remove the cobia from the marinade, pat it dry with paper towels and slice it into thin pieces. 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. Season to taste.
To plate, spread a layer of the avocado coulis on the bottom of 4 wide bowls and top with equal portions of the salad. Scrape the granita into 4 portions, each about the size of a golf ball, and top the salads with the the granita. Garnish with the lemon basil and jalapeno. Serve immediately.
This recipe was provided by a chef, restaurant or culinary professional and makes a large quantity. The Food Network Kitchens have not tested it for home use and therefore cannot make any representation as to the results.