In a high-speed blender or food processor, add the celery and carrots and blend or pulse until finely chopped. Scrape down the sides and under the blade, then add the onion and repeat. If any big chunks remain, just scrape down the sides and blend again or hand chop it.
In a large pot, warm the oil over medium heat. Add the onion/carrot/celery mixture and 1 teaspoon salt. Cook for 3-5 minutes or until softened and water has evaporated.
Add the garlic, oregano, fennel, and black pepper and cook for 30 more seconds, stirring often. Add the water, chickpeas, and remaining 1 teaspoon salt. Increase the heat to high and bring to a boil. Once it starts boiling, reduce the heat to maintain a simmer. Add about 2 cups of the chickpeas and broth to the high-speed blender (get plenty of chickpeas in there to help thicken the soup) and blend until thickened. Stir it back into the pot along with the potato and kale (if the kale is too much for the pot, add it in batches).
Increase the heat to high to bring it back to a boil, then reduce the heat to medium-low and simmer rapidly for 20-25 minutes, stirring halfway through, or until the potato is cooked through and liquid has reduced to a stew-like consistency. Remove from heat and stir in the lemon and half of the parmesan. Taste and add more salt or lemon, if needed.
Serve topped generously with remaining parmesan, olive oil, black pepper.