Place beans in a large bowl and add enough water to cover by 2 inches. Soak until beans are pale yellow and split apart when rubbed between fingertips, 12 to 18 hours.
Drain and rinse beans (you should have about 3 cups of beans). Working in batches, process 1 cup soaked soybeans with 3 cups water in a blender until mostly smooth, about 3 minutes. Transfer mixture to a large dutch oven and repeat twice with the remaining 2 cups of beans and 6 cups of water.
Line a colander with butter muslin or a triple layer of cheesecloth and set over a large bowl. Bring soy mixture to a boil over medium-high heat, stirring frequently with a rubber spatula to prevent scorching and boiling over. Reduce heat to medium-low and simmer, stirring frequently, until slightly thickened, about 10 minutes.
Pour soybean mixture into prepared colander to strain. Carefully pull edges of muslin together to form a pouch and twist edges of muslin together. Using tongs, firmly squeeze soybean pulp to extract as much liquid as possible. You should have about 8 cups of soy milk; discard soybean pulp or reserve for another use. Transfer soy milk back to clean dutch oven and bring to a boil over medium-high heat, stirring occasionally to prevent scorching. Remove pot from heat.
Combine remaining 1/2 cup water and nigari in a measuring cup. Begin stirring soy milk in a fast, figure-eight motion with a rubber spatula. While still stirring, add 1/4 cup prepared nigari mixture. Stop stirring and wait until the soy milk stops moving. Cover the pot and let it sit undisturbed for 2 minutes. Uncover, add remaining nigari mixture and gently stir in a figure-eight motion 6 more times. Cover the pot and let it sit until curds form, around 20 minutes.
Line tofu mold with butter muslin or a triple layer of cheesecloth and place it in a large colander or baking dish. Using a slotted spoon or small fine mesh strainer, gently transfer soy milk curds to the prepared mold. Cover the top of the curds with excess muslin and the top of the tofu press. Place a 2 pound weight (or similar) on top to assist with pressing. Press tofu until desired firmness is reached. 20 minutes for soft, 30 minutes for medium, 50 minutes for firm (you can also leave it for longer; I let mine press for over 2 hours).
Carefully remove tofu from mold and place in a baking dish. Fill with cold water to cover and let sit until tofu is slightly firmer, about 10 minutes. Tofu can be refrigerated in an airtight container for up to 1 week; change water daily.