1.Pour the dried beans onto a rimmed baking sheet and pick through them, removing and discarding any broken beans or stones. Place the beans in a large nonreactive bowl and cover them with at least 2 inches of cold water. Allow to soak for 12 to 24 hours.
2.Meanwhile, prepare the mold. Take the milk carton and cut off one of the long sides (try to keep the piece you cut off in a rectangle shape so it can be used later).
3.Place the cut piece in a resealable plastic bag and set it aside. Using a hole punch, a skewer, or scissors, poke 1/2-inch holes all over the milk carton so that the tofu can drain easily.
4.Reinforce the sides of the mold by running tape around the perimeter of the carton. Line the mold with doubled-over cheesecloth and trim the cheesecloth so there are just a few inches overhanging on each side. Fill a resealable plastic bag with about 1 pound of pie weights or dried beans. Set everything aside until the beans are done soaking.
5.Once the beans have soaked, drain them and discard the water. Place half of the beans (about 3 cups) in a food processor and pour in enough water to just cover the mixture (about 1 to 1 1/2 cups).
6.Process the mixture until it is pulverized and smooth, about 30 seconds. Then repeat with the remaining beans.
7.Place all the pulverized beans in a large (15- to 20-quart) stockpot and add 10 cups water. Bring the mixture to a simmer over medium heat. Set 2 cups of water nearby to pour over the mixture later on.
8.Stir the mixture occasionally and let it simmer. The mixture is ready when foam rises to the top of the pot, about 25 to 30 minutes.
9.Remove from heat, immediately pour in the reserved 2 cups water, and stir until the foam subsides—it will not completely disappear.
10.Place a large fine mesh strainer in a bowl and strain the mixture. Push on the pulverized bean solids so that most of the liquid drains out. Discard the solids (known as okara) or use in a recipe that calls for them. The liquid is soy milk. It will last up to three days refrigerated.