How to Make It
Bring a large, heavy pot of water to a boil. Add the lobsters and cook for 5 minutes; the water does not need to return to a boil. Transfer the lobsters to 2 large rimmed baking sheets. Drain the pot. When the lobsters are cool enough to handle, twist off the tails and claws. Break the bodies and little legs into 3-inch pieces. Using scissors, cut down the center of the tail shells and remove the tails in one piece. Cut down the length of each tail and discard the dark intestinal veins. Crack the claws and remove the meat in one piece. Cover and refrigerate the lobster meat.
Heat 1/4 cup plus 2 tablespoons of olive oil in the large pot. Add the lobster body pieces and legs and cook over high heat, stirring often, until beginning to brown, about 7 minutes. Add the garlic, carrots and onions and cook over high heat, stirring occasionally, until the onions are softened, about 8 minutes. Add the tomatoes and cook until any liquid has evaporated, about 5 minutes. Add the pimentón and cook, stirring, until fragrant, about 3 minutes. Add the brandy and cook until almost evaporated, about 3 minutes. Add the water and bring to a boil. Simmer over moderate heat for 30 minutes, skimming a few times. Strain the lobster stock into a large saucepan. Bring the stock to a simmer, cover and keep hot.
Preheat the oven to 400°. Wash out the large pot and return it to the stove. Slice the lobster tails crosswise 1/2 inch thick and transfer the slices to a large rimmed baking sheet, fanning them slightly. Put the claw meat on the baking sheet. In a small bowl, combine the melted butter with 1 tablespoon of the olive oil; brush over the lobster and season with salt and pepper. Cover with foil and bake for about 12 minutes, until just heated through.
Meanwhile, in the large pot, heat the remaining 1/4 cup plus 2 tablespoons of olive oil until shimmering. Add the fideos and cook over moderately high heat, stirring constantly, until browned, about 5 minutes. Stir in half of the lobster stock, cover and cook for 3 minutes. Add half of the remaining stock, cover and cook until almost absorbed, about 3 minutes. Add the remaining stock and cook, stirring, until the fideos are al dente, about 2 minutes longer. Season with salt and pepper.
Spoon the fideos into shallow bowls, top with the lobster and serve.