Place all the ingredients except the nondairy milk in a bowl or the bowl of a stand mixer. Drizzle in the milk as needed until the dough comes together. Knead it just until it's soft and pliable and smooth.
Form the dough into a smooth ball and place in a bowl to rise, turning over the dough once to coat the top with the oil. Cover the bowl with a tight lid or cling wrap and let stand in a warm place for four hours or overnight in the refrigerator, until the dough has doubled. This dough won't rise as fast or as much as a bread dough with added yeast would, but that's fine.
If you placed your dough in the refrigerator, and it hasn't doubled overnight, let it stand in a warm place in your kitchen until it does.
Knead the risen dough, and divide into 12 portions. Shape each into a smooth ball by stretching the dough and tucking the sides underneath. Place in a well-oiled 13 X 9 inch baking pan. The rolls won't touch at this point but that's okay because they will as they rise and bake.
Cover the pan with a kitchen towel and place in a warm spot, like the oven with just the pilot light turned on, for four hours or until they are all puffy and are touching each other.
Preheat the oven to 350 degrees (make sure you remove the rolls from the oven if they are rising in there while the oven preheats)
Place the baking sheet in the oven and bake 30 minutes until the rolls are golden-brown on top. Let them stand on a rack 20 minutes, then remove from the rack and continue cooling.