Place the roughly chopped potatoes and 1/2 tbsp water in a microwave-safe container. Cover loosely with plastic wrap and microwave at 600W for 5 minutes. Mash the potatoes in a food processor until smooth while still hot.

In a saucepan, combine butter, salt, and water. Heat until boiling, then remove from heat and add the flour. Mix well until combined.

Gradually add the beaten egg to the dough, mixing thoroughly after each addition. Add the mashed potatoes and grated cheese, and mix well.

Shape the mixture into bite-sized balls.