Preheat the oven to 400 degrees F; position an oven rack in the middle of the oven.
Poke holes in the potatoes, then place them on a rimmed baking sheet and bake until just soft, about 45 minutes.
Meanwhile, place the lobsters in the freezer for 15 to 20 minutes—this will put the lobsters to sleep and calm them down so they're not so acrobatic when you try to finish them off. Fill a large pot with water and add enough salt so the water tastes like seawater, then bring to a boil. Fill a very large bowl with ice and water.
Working with one lobster at a time, in one decisive motion, plunge a chef's knife into and all the way through the lobster's head so the head is halved vertically—this kills it quickly. Break down the lobster by removing the claws and the tail. Discard the lobster carcasses or save them to make lobster stock later.
Add the lobster tails to the boiling water and cook for 3 minutes, then add the claws and cook for an additional 6 to 7 minutes. Remove the lobster from the boiling water and set aside. Once cool, crack the claws and tails and remove the meat. Quarter the tails lengthwise and chop. Cut the claw meat in half and chop it into pieces the same size as the tail meat.
Let the potatoes cool slightly; leave the oven on. Carefully, without breaking the skin, slice the potatoes in half and scoop the flesh into a bowl. Reserve for later.
In a medium saucepan, melt the butter over medium heat and cook until the milk solids sink to the bottom of the pan and turn hazelnut brown and the butter starts to smell nutty, 3 to 4 minutes. Add the rosemary and cook, stirring, until fragrant, about 1 minute. Add the scallions and cook, stirring, for 1 minute. Add the scooped potato flesh, salt and pepper to the saucepan and stir to combine. Add the chopped lobster, creme fraiche and 3/4 cup of the Gruyere. Mix until thoroughly combined.
Spoon the potato-lobster mixture into the potato shells and place them in a 9-by-13-inch baking pan or on a quarter-sheet tray. Sprinkle the potatoes with the remaining 1/4 cup Gruyere and bake until the potatoes are hot and bubbling, 12 to 15 minutes. Top with the scallions, and serve.