Preheat the oven to 375 degrees. Place the tomatoes and fennel on a parchment-lined baking sheet. Toss the veggies with a ¼ of the oil and salt and roast for twenty minutes.
Next cook the lobsters: Bring two inches of water to a boil over high heat in a very large pot. Add the lobsters and hold down the lid to kill them quickly. Steam them for twelve minutes.
Remove the lobster meat from the shells, and chop it all in half inch pieces. Set aside.
Bring a large pot of water to a boil for the pasta. Add the 3 tablespoons of kosher salt and cook the fettuccini until it's al dente. Drain it well.
In a large skillet, on low heat, add the rest of the oil and cook the garlic until it's soft. Stir in the red pepper flakes and salt. Stir in the lobster, and the roasted tomatoes and fennel. Top with the basil.