In a large pot over high heat, combine potatoes, onions, and water to cover. Boil for 30 to 45 minutes, or until tender. Drain the mixture, reserving 3 cups of the cooking liquid. Transfer this in small batches to a blender and puree until smooth.

In the same pot over medium heat, combine flour and butter, stirring together well, to form a roux. Slowly add milk, stirring constantly, until well blended.

Reduce heat to low and add the puréed potato mixture. Let simmer, stirring occasionally for 5 to 10 minutes.