From The Practical Housekeeper 1855
This is essentially the way that we make potato soup at our house and we like it very much.
Modern directions: Chop 1 - 2 potatoes for each person. Potatoes should be in nice bite sized pieces. Boil in salted water for 5 minutes or until just soft enough to mash with a fork. Do not overcook. Drain and set aside. Melt a good amount of butter in a pan. Mix 2 tablespoons of flour in one cup of milk. Add this to the butter. Heat until thickening starts. Stir constantly. Add the cooked potatoes. Add more flour mixed in milk until it covers the potatoes. Set heat to high and stir every 1-2 minutes. When thickening becomes frothy it is done. Salt and pepper to taste. You may use broth instead of milk. Onions sauteed in the butter at the beginning is also very good.
The main difference is that we make it with milk or broth instead of using the cook water. We also generally make this in very large batches and do not serve it over toast. The toast idea is very interesting and tasty if you have stale bread that needs to be used up.