Place deveined kale in a colander and run under cool water. While the water is running, knead or wring the kale leaves in your hands to effectively break down the tough fibers of the leaf. The pale, dusty look of the kale will change to a glossy dark green color. Place the kale in a clean kitchen towel and wring out as much water as possible.
To make the dressing, whisk lime juice, extra virgin olive oil, salt and pepper in a large bowl until it comes together and forms an emulsion.
Place finely chopped cabbage into the bowl of a food processor and pulse 4–5 times to coarsely chop. Pour the cabbage into the bowl containing the dressing. Chop the kale in the food processor again using only 4–5 pulses and add it to the cabbage.
Combine the kale and cabbage with the dressing. Sprinkle with Parmesan cheese and taste for seasoning.