Preheat oven to 375 degrees F. Boil pasta and according to the directions on the package for al dente, 6 to 8 minutes; drain.
Meanwhile, melt ¼ cup butter in a large saucepan set over medium heat. Whisk in flour and cook 2-3 minutes, until golden brown. Slowly add milk, whisking until combined.
Season with salt, pepper, and nutmeg, then simmer 2-3 minutes until thickened. Remove the pan from the heat.
Stir in 12 ounces Gruyere, all Cheddar, and ¼ cup Parmesan cheeses, whisking until smooth. Gently stir in cooked pasta and lobster, then transfer to a 9x13 baking dish. Top with remaining Gruyere.
In a small bowl, melt remaining 2 tablespoons of butter, then stir in Panko and remaining Parmesan. Sprinkle over contents of baking dish, season with salt and pepper as desired, and bake for 20-30 minutes until browned and bubbly. Garnish with fresh parsley and serve immediately.
Notes
Reheating instructionsIf frozen, make sure to thaw and reheat in your oven at 350 degrees F for about 30 minutes. If refrigerated, you can reheat in the oven for 15 to 20 minutes. When reheating in the microwave, cover the dish with a bit of melted butter or oil for moisture.