Fill a large pot with water and bring it to a rolling boil. Add the lobsters and cook for 8-10 minutes until shells turn bright red. Remove and transfer to an ice bath. Extract meat and chop into bite-sized pieces.

In a medium saucepan, melt butter over medium heat. Add minced shallots and sauté for 3 minutes. Whisk in flour to create a roux and cook for another minute. Gradually add cream and stir until thickened. Mix in grated cheese until melted and smooth.

Remove sauce from heat and fold in chopped lobster meat. Season with salt, pepper, and paprika.

Preheat broiler to high. Spoon lobster and cheese mixture into a serving dish and top with breadcrumbs. Broil for 5-7 minutes until topping is golden brown.

Remove from the oven, let cool for a minute, and optionally garnish with parsley. Serve hot with garlic bread and a simple green salad.