In a large bowl, cover the soy beans with 3 inches of cold water. Cover and let stand overnight at room temperature. Drain the soy beans and transfer them to a blender. Add 3 cups of the filtered water and puree at high speed until as smooth as possible.
Line a large sieve with a clean cotton napkin or 3 layers of cheesecloth and set the sieve over a heatproof bowl. In a large pot, bring 3 cups of the filtered water to a boil. Add the soy bean puree and bring just to a boil (be careful not to let it boil over). Boil over moderately high heat for exactly 8 minutes, stirring constantly with a heatproof rubber spatula to prevent sticking and scorching.
Carefully pour the mixture into the prepared sieve. Let stand until just cool enough to handle, about 20 minutes. Gather the ends of the napkin or cheesecloth and squeeze to extract as much of the soy milk as possible; the remaining solids should be nearly dry. Discard the solids and skim off any foam from the soy milk. You should have about 4 cups of soy milk.
In a small measuring cup, dissolve the nigari in the remaining 1/4 cup of filtered water. Spoon 2 tablespoons plus 2 teaspoons of the nigari solution into a large heatproof glass bowl. In a clean large saucepan, heat the soy milk to 185°. Gently pour the hot soy milk into the bowl with the nigari solution and quickly stir once or twice just to combine thoroughly; it's easy to scramble the rapidly coagulating tofu. Cover and let stand undisturbed until the silken tofu is fully set, about 5 minutes. Discard the remaining nigari solution. Serve.
Nigari can be purchased at Japanese markets and online at myworldhut.com.