Coarsely puree the beans with their liquid in a food processor or loosely covered blender. Pour into a medium-size (2- to 3-quart) saucepan set over medium heat. Add enough water to thin to the consistency of a medium cream soup and bring to a simmer. Taste and season with salt, usually about ½ teaspoon. Keep warm.
In a skillet, cook the chorizo over medium-low heat until browned and done, about 10 minutes, breaking up any clumps as it cooks. Drain off the rendered fat, cover the skillet and keep warm over very low heat.
Soften the tortillas by quick-frying them one by one in a skillet liberally filmed with oil. Or steam them in a microwave by wetting a paper towel, wringing it out, wrapping it around the tortillas and sliding the package into a plastic bag (don’t seal). Heat in the microwave at 100% power for 45 seconds.
One by one, dip both sides of the warm tortillas into the sauce, fold into quarters and transfer to a warm serving platter or 4 individual plates, laying the tortillas slightly overlapping. Spoon the remainder of the hot sauce over the folded tortillas (there should be a considerable amount of sauce), strew with the warm chorizo, splash with the (optional) salsa, then sprinkle on the crumbled cheese, chopped parsley and the sliced onion. Serve your delicious enfrijoladas without hesitation—they don’t take well to delays.