Bring a large stock pot of salted water to a boil, and then poach the lobsters for 1 minute. Cool immediately in an ice bath, and then remove and separate the lobster heads from the bodies. Trim the gills and chop the lobster heads into small pieces, split the tails in half lengthwise, and remove the claw and knuckle meat from the shells. Toss all the lobster pieces with 1/2 cup of the olive oil, 1 tablespoon of the ginger and the minced lemongrass in a bowl to marinate. Transfer to the refrigerator.
Heat a large pot over high heat. Pour in the remaining olive oil and add the basil stems, roughly chopped fennel, garlic, bay leaf, leeks, onions, parsley and thyme and cook, stirring, until softened but not browned, 7 to 8 minutes. Add the lobster heads and cook, stirring, for 12 to 15 minutes, and then stir in the tomato puree and continue cooking for 3 to 4 minutes. Add the white wine, remaining ginger, remaining lemongrass, the salt, coriander, fennel seeds, white peppercorns and star anise and cover with water by 1 inch. Bring to a boil, and then reduce to a simmer and cook uncovered for 35 minutes.
Strain the broth through a fine-mesh sieve into a very large wide pot, using a ladle to press against the solids to remove all of the liquid; discard the solids. Bring the broth to a boil over medium-high heat, and then add the fennel wedges, potatoes and pre-cooked lotus root slices and cook until softened, 10 to 15 minutes. Remove the marinated lobster tails and claws and add to the pot along with the mushrooms, Thai basil leaves and green basil leaves. Season the bouillabaisse with salt and black pepper.
Divide the bouillabaisse among 4 shallow bowls, and finish the dish with some sauteed water spinach, grilled scallions, and slices of grilled baguette, if desired.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.