Prepare an 8- or 9- by 5-inch bread pan. Spray or coat lightly with oil, then flour the pan.
In a large mixing bowl, stir together all dry ingredients until completely mixed.
In a smaller mixing bowl, mash the tofu well until it resembles small-curd cottage cheese. Add the remaining wet ingredients and mix until thoroughly combined.
Pour the wet mixture into the dry and stir together. If you need a bit more to moisten all the dry ingredients, add 1 tablespoon additional nondairy milk at a time, but let the dough remain stiff. Don't overbeat.
Transfer the dough to the prepared loaf pan, Use a large flat spoon to spread the stiff dough, then flatten lightly once it's all in the pan.
Bake for 35 to 40 minutes, or until the top is a lovely golden brown, and a small knife inserted into the center comes out clean.