How to Make It
Using kitchen scissors, cut down the center of the lobster tail shells; remove the meat from the shells. Halve the lobster tails lengthwise and remove the intestinal veins. Slice the lobster tails crosswise 1/2 inch thick and pat dry.
In a large, deep skillet, heat 2 tablespoons of the olive oil until shimmering. Add the lobster (or shrimp, if using) to the pan, season with salt and pepper and cook over high heat, stirring occasionally, until lightly browned and almost cooked through, about 4 minutes. Transfer the lobster to a plate.
Add 1 tablespoon of the oil to the skillet. Add the garlic and chile and cook over high heat for 1 minute. Add the wine and bring to a boil, scraping up any browned bits from the bottom of the pan. Simmer until the wine has reduced to 1 tablespoon, about 6 minutes. Add the remaining 5 tablespoons of olive oil and the tomato to the skillet and cook, stirring, for 1 minute.
Meanwhile, cook the pasta in boiling salted water until al dente. Drain, reserving 1/2 cup of the cooking water. Add the pasta, lobster and basil to the skillet and toss; add a few tablespoons of the cooking water if the pasta seems dry. Season with salt and pepper, transfer to a large bowl and serve.