Cook, bake, or microwave the potatoes in their skins until done but still firm. When cool enough to handle, peel, and slice about ¼-inch thick. If the potatoes are organic and you've scrubbed them really well, you can leave on the peel.
Preheat the oven to 375º F.
Heat the oil or vegan buttery spread in a medium skillet. Add the onions and sauté over medium heat until soft and golden.
Combine the tofu or beans, half of the onions, and the rice milk in a food processor until very smooth. Set the remaining onions aside.
Transfer the mixture from the food processor to a large mixing bowl and add the potato slices. Stir together thoroughly but gently (don’t worry if the potato slices break apart). Season with salt and pepper. If it seems like there's too much sauce for the potatoes, don't worry — a lot of it gets absorbed while baking.
Transfer the mixture to a lightly oiled large shallow round, square, or oblong baking dish and pat it in evenly. Top with the reserved onions, followed by optional breadcrumbs and the paprika.
Bake until the top is golden and slightly crusty, about 30 to 40 minutes. Let cool for 5 minutes, then cut into squares or wedges to serve.