In a Dutch oven or similar large pot, heat the oil over medium-high heat. Once it’s hot and shimmering, the onion, carrots, salt, and pepper. Cook, stirring occasionally, until the onion is turning translucent, about 5 minutes.
Add the garlic and chickpeas. Stir and cook for 30 seconds.
Add the broth, potato, bayleaf, and rosemary. Increase the heat to bring the soup to a boil, then reduce the heat and let simmer for 15 minutes, until the potatoes are tender.
Fish out and discard the bayleaf. With an immersion blender, lightly puree the soup, leaving a good number of the chickpeas intact (this will thicken the soup—you can also blend a few ladles of the soup in a regular blender, then add it back to the pot). Stir, partially cover the pot, and simmer 10 minutes to reduce. Stir every few minutes, scraping along the bottom of the pot to prevent sticking.
Stir in the kale, lemon juice, and Parmesan. Let simmer until the kale is tender, 3 to 5 minutes. Taste and adjust the salt and pepper as desired. Serve hot with a sprinkle of additional Parmesan.