How to Make It
Boil the lobsters until just red but still undercooked, 4 minutes; let cool. Remove the meat from the tails, claws and knuckles; discard the intestinal veins and cut the tails into thick slices. Put the meat in a bowl and refrigerate. Chop the bodies and legs.
In a heatproof bowl, cover the chiles with the boiling water and let stand for 15 minutes. Meanwhile, in a pot, heat the oil. Add the chopped shells and cook over high heat for 1 minute. Reduce the heat to moderate and cook, stirring, until browned. Stir in the tomato paste and cook for 1 minute. Add the brandy and simmer for 2 minutes, scraping up any browned bits. Add the onions, carrots, fennel and garlic; cook over low heat for 5 minutes.
Lift the chiles from the bowl and mince; add with the soaking liquid to the pot. Add the stock and basil; bring to a boil. Cover partially and simmer for 2 hours. Strain the stock. Add the saffron and let stand for 20 minutes.
In a small heatproof bowl, cover the ñora chile pepper with the boiling water and let stand until softened, about 15 minutes. Lift the pepper from the water and finely chop it. Return the chopped pepper to the soaking liquid.
In a medium skillet, heat the olive oil. Add the onion and cook over moderate heat until translucent, about 4 minutes. Add the garlic, bell pepper, tomatoes, vinegar and the chopped ñora pepper and its soaking liquid. Simmer over low heat, stirring occasionally, until the liquid has evaporated and the vegetables are very soft and browned, about 20 minutes. Season with salt and pepper. You should have about 1 cup.
Light a hardwood charcoal or wood fire in a covered grill. When the fire is very hot, set a 17-inch paella pan on the grill. Add the olive oil and heat until shimmering. Season the chicken with salt and pepper and cook until browned, about 4 minutes per side. Transfer the chicken to a plate. Add 3 cups of the warm stock to the pan, scraping up the browned bits on the bottom. Whisk in the 1 cup of sofrito and bring to a rolling boil. Add the rice and romano beans, shaking the pan to distribute them evenly. Season with salt and return to a vigorous boil. Cook for 4 minutes, stirring as little as possible; add more lit coals and/or wood to the fire to maintain the temperature. Bury the chicken pieces skin side up in the rice and cook until the stock is nearly evaporated, about 6 minutes.
Reduce the heat to a simmer; if necessary, use cast-iron trivets to lift the pan higher off the grill to reduce the heat. Add 3 more cups of the stock, 1 cup at a time, shaking the pan from time to time and waiting until the stock is nearly absorbed between additions, 10 minutes. The rice should be lightly browned and crisp on the bottom, but not burned. Continue to cook the paella, adding as much of the remaining hot stock as necessary, 1/2 cup at a time, until the rice is almost tender and still very moist, 5 minutes. Nestle the clams and mussels into the rice, cover the grill and cook until they start to open, 6 minutes. Arrange the lobster all over the paella. Cover and cook until the clams and mussels are wide open and the lobster is heated through, 3 minutes longer.
In a blender, puree the garlic, egg, vinegar, lemon juice and salt at high speed. With the blender at low speed, add the canola oil in a thin stream and blend until the sauce is creamy, then drizzle in the olive oil until blended. Serve right away or lightly chilled.
Transfer the paella to the table, cover with a kitchen towel and let stand for 5 minutes. Serve with the allioli and lemon wedges.
The garlic mayonnaise can be refrigerated overnight.
Dried ñora chile peppers and Bomba and Calasparra rice are available at specialty stores or online at tienda.com.