Peel and boil potatoes. Drain, and mash coarsely. Mix in egg, cream and seasonings.
Place flour in a large mixing bowl. Add potato mixture. Using a spatula, mix well. If sticky, add more flour. The dough should be soft but not elastic. On a work surface, form the mass into a log.
Divide the log into smaller portions and using your hands, roll out into 1/2-inch-long pieces.
Dust them well with flour. Hold a flour-dusted fork, concave side up, in one hand. With the other hand, push a piece of dough into the tines, making an indentation with your thumb. Then roll the dough off the tines, making a shape like a tiny bowl with ridges on the bottom. Flour the fork and repeat with rest of dough.
Sauce:
Saute chives in butter and a tablespoon water and vinegar. Simmer for 2 minutes Add cream. Simmer 10 minutes. Cook gnocchi in boiling water for 4 to 5 minutes.
Drain. Stir in the chive sauce. Heat and serve with Parmesan cheese.