In a stockpot over high heat, boil potatoes in salted water for 10-15 minutes, or until cooked through.
Drain potatoes, press through ricer (see notes,) and using a fork mash together with butter.
Whisk together eggs, basil, salt, pepper and a little flour, add to mashed potatoes and combine. Add more flour as you go until you have a smooth firm dough.
Divide dough into small dumplings, about the size of a regular meatball.