Preheat oven to 450°F and oil a large shallow glass baking dish.
Slice Parmesan cheese and butter into thin slices (freezing the stick of butter first makes this easier).
Rinse, scrub, and peel the potatoes.
Place a peeled potato on a cutting board and place one long handled wooden chopsticks or wooden spoons on each side of the potato lengthwise.
use a sharp knife and slice each potato crosswise, making 1/4" apart slices, cutting down vertically. The chopsticks will prevent the knife from cutting entirely through the potato.
Place a slice of Parmesan in the first crevice of a potato. Place a slice of butter in the second crevice. Continue to alternate Parmesan and butter until all crevices are filled.
Sprinkle with paprika.
Drizzle with heaving whipping cream.
Bake for 35 to 40 minutes in the preheated oven.
Remove from the oven, drizzle with the remaining butter, and sprinkle bread crumbs onto the tops.
Return to the oven and bake for an additional 20 minutes, or until nicely browned.