1. 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.
2. In a small bowl, mix together 3 cups cheese and the cream. Set aside.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.