Preheat oven to 350 degrees F. In a medium saucepan melt 4 tablespoons of butter over low heat. Add flour and stir to combine. Cook, stirring constantly, for 3 minutes. Increase the heat to medium and, with a wire whisk, gradually add the half and half. Cook 3-5 minutes, or until thickened, stir often. Remove from the heat, and add 1/2 cup Parmigiano-Reggiano, 1/2 cup gruyere cheese, garlic, 3/4 teaspoon each of salt and pepper. Stir until cheese is melted and well combined. Cover and let stand.
Fill a large pan with water and bring to a rolling boil over high heat. Add 1 teaspoon salt. Add pasta, return to a boil, reduce the heat to a low boil and cook for about 8-10 minutes, or until just undercooked. Drain water from pasta and return to the pan. Add the bechamel sauce and 2 tablespoons butter; stir until well combined. Set aside.
In a large bowl combine the sharp cheddar cheese and monterey jack cheese, and 1 cup of the Parmigiano-Reggiano cheese. Spray a 3-quart baking dish with non-stick cooking spray. Place one half of the pasta in the baking dish. Top with half of the mixed cheeses. Top with the other half of the pasta, followed by the remaining mixed cheeses. Bake in a pre-heated oven for 35-40 minutes, or until visibly bubbling and hot.
While pasta is baking, combine 1 1/2 tablespoons butter and lobster meat in a medium saucepan, over medium-low heat for 3 minutes, or until lobster is heated through. Remove from heat; add bread crumbs, green onions, paprika, basil and thyme, and 1 ounce of Parmigiano-Reggiano. Toss lightly to combine.
Remove the baking dish from the oven and spoon the lobster mixture over the top of the pasta. Spread evenly.
Turn the oven to "Broil" and return the baking dish to the oven. Allow to broil 10-12 minutes or until the top is golden brown. Let stand 5 minutes before serving.