Water pie is a simple pie that was reportedly popular during the Great Depression, although I can find no documentation of this popularity. It is quite popular on current baking websites, however, and is universally reported as a delightful Depression-era treat, sometimes alternatively named 'depression pie'. It is essentially a shortbread pie, or a large, gooey sugar cookie with a crust.
To make a water pie, you get yourself a pie crust, and fill it with about a cup and a half of water. Sprinkle in about four cups of flour and one cup of sugar; do not mix it. Add seasoning (usually vanilla, sometimes cinnamon and/or nutmeg), and then slice pats of butter to place on top; usually about 5 tablespoons worth. Again, don't stir.
Stick it in the oven at 400°F (200°C) for 30 minutes, and then reduce heat to 375°F (190°C) for another 30. You may need to cover the sides of the crust at this point, to prevent burning. Remove from oven, and allow it to cool. As it cools it will solidify; it is usual to then move it to the fridge to solidify a bit more before eating, served chilled. However, if the massive economic collapse and difficulty of procuring ice has deprived you of the wonders of the modern kitchen, it'll probably be okay at room temperature.
Unfortunately, I have been completely unable to determine if this recipe is a modern invention with a modern myth to make it more flavorful, or simply a recipe that no-one thought was special enough to write down in the 1930s. If you have any leads, please let me know.