Thinly slice the red onion and place it in a small bowl of cold water with a splash of the red wine vinegar. Let it soak for 15 minutes to mellow the raw bite.
Cut the stale rye bread into 1.5 cm cubes and add to a mixing bowl. If the bread is very hard, sprinkle it with a tablespoon or two of cold water and let it sit for 2 minutes, it should soften slightly but still hold its shape.
Cut the Casera cheese into cubes the same size as the bread, about 1.5 cm, and add to the bowl.
Drain the onion well and add it to the bread and cheese.
Drizzle the olive oil and remaining red wine vinegar over the mixture. Season with salt and pepper.
Toss gently with your hands or two spoons until everything is coated and the cheese and bread are evenly mixed.
Let the salad rest at room temperature for 10 minutes so the bread soaks up the dressing without turning mushy.
Scatter the chopped parsley over the top and serve in the bowl, or divide among plates.