The secret to the dish is in the sauce, and it's all about reserving the roe from the lobster, which is mixed with punchy garlic, bright parsley, and a swig of brandy. A few other tricks are to use the lobster antenna to remove the sand and veins from the lobster itself and to make a fire using manzanilla (chamomile) branches.
To kill the lobsters, hold each one firmly on a cutting board with its head toward you, plunge a sharp heavy knife into the center of the head, and quickly bring the knife down to the board, splitting the front of the lobster in half; turn it around and cut it completely in half. Pull off the tails, and then pull off the claws if using Maine lobsters. Slice the tails into ½ inch medallions, cutting through the natural segments in the shells. Remove the roe from the heads and reserve; remove and discard the head sacs and tomalley.
Heat 6 tablespoons of the olive oil in a paella pan or a large sauté pan over high heat. Add the lobster heads, claws if you have them, and tailpieces and sauté for 1 minute, or until they turn red. Transfer the heads and claws to one bowl and the tail pieces to another. Add the onion, tomatoes, peppers, and half the garlic to the pan and cook until softened, 8 to 10 minutes. Add 8 cups water, bring to a boil, and season with salt and pepper. Add the lobster heads and claws and simmer for 10 minutes. Add the tail pieces and cook for 3 to 5 minutes, until opaque throughout. Remove the stew from the heat and let rest while you make the sauce.
Combine the reserved roe, the remaining 2 tablespoons oil, the remaining garlic, the parsley, and brandy in a mortar and mash to a loose paste with the pestle. Add to the stew and stir well, then check for seasoning and serve.