Preheat oven to 350°. Set potatoes on a baking sheet and slash each deeply lengthwise down the center. Bake potatoes until they are tender and look slightly dried out, 1 1/4 to 1 1/2 hours.
In a small bowl, mix together 3 cups cheese and the cream. Set aside.
As soon as potatoes are cool enough to handle, peel them; discard peels. Put potatoes through a potato ricer into a large bowl. Mix in egg, salt, and 1 cup flour, adding just enough additional flour to make the dough pliable and not sticky (too much flour will make the gnocchi heavy). Turn out onto a floured work surface; with floured hands, knead dough 10 to 12 times.
Divide dough and cover one batch with a damp kitchen towel. Roll other batch into a 3/4-in.-thick rope and cut into 3/4-in.-long pieces. Roll each piece into a ball, then flatten into a 2-in. circle with your fingers or the bottom of a well-floured drinking glass.
Bring a large pot of salted water to a boil. Top each dough circle with 1/2 tsp. cheese-cream mixture. Gather up dough around filling and pinch to close, then roll into a small, smooth ball. Repeat rolling, filling, and forming with second batch of dough.
Preheat broiler with rack 4 in. below heating element. Divide melted butter between two 2-qt. casserole dishes (or use one 4-qt. casserole and all the butter). Working in batches, drop gnocchi into boiling water, being careful not to crowd them. Boil gnocchi until they rise to the surface, 4 to 5 minutes; cook 8 to 10 seconds longer, then transfer with a slotted spoon to casserole dish(es), making sure water drains off from gnocchi.
Turn gnocchi to coat in butter. Sprinkle with pepper and remaining cheese and broil until browned on top, 5 minutes. Sprinkle with parsley and serve immediately.
Note: Nutritional analysis is per main-course serving.