Heat the olive oil in a large stockpot over medium heat. Brown the chorizo in the oil, 5 to 7 minutes. Add the potatoes, onions, garlic and chicken broth.
Simmer until the potatoes are fork tender, 20 to 25 minutes. Reduce the heat to low, add the kale, and cover. Cook until the kale wilts, 7 to 10 minutes.
Uncover, add the Parmesan, and heat through for about 5 more minutes. Season to taste with salt and pepper.