Make mashed potatoes by combining the potato pearls and hot water. Stir and let set up. Cool.
To make the pate a choux: Combine the water, butter, salt and sugar in a saucepan and bring to a rolling boil. Add the flour all at once, stirring constantly, until the mixture forms a ball and pulls away from the side of the pan.
Transfer the mixture to the bowl of an electric mixer, and using the paddle attachment on high speed, beat in the eggs one at a time, fully incorporating and scraping down the sides of the bowl after each addition. Check the appearance and consistency after each addition. When the dough is a medium-stiff paste and has a shiny appearance, stop adding eggs.
To make croquettes: Combine 16 ounces mashed potatoes and 4 ounces pate a choux
Form a #70 scoop of mixture around one cube of cheese. Shape into ball. Repeat with remaining ingredients. Chill balls until firm.
Bread croquettes using standard breading procedure. Refrigerate. (Croquettes may be frozen at this point. Place in tightly sealed container. Freeze.)