Poke both types of potatoes all over, with a fork, and microwave in five-minute intervals, flipping the potatoes between each interval until the potatoes are soft, about 10–15 minutes. When potatoes are cool enough to handle, peel and discard the skin and then mash the potatoes with a fork. Combine mashed sweet potato and beaten egg in a bowl and then season to taste, with salt and pepper. Add flour, 1/4 cup at a time, and knead until a dough forms.

Bring a large pot of salted water to a boil. Blanch the gnocchi in batches (they are done when they float to the surface).

Melt the butter in a skillet over medium-high heat. When melted, add the cooked dumplings and toss to coat with butter. Top with grated parmesan and serve.