Put a large stockpot over a medium flame and heat the oil. Add the carrots, leeks and celery and cook until softened, about 5-7 minutes.
Add in the potatoes and tomatoes and bit of salt and cook for 5 minutes while stirring occasionally.
Add the chicken broth or the water with 2 boullion cubes to the pot. Bring to a boil and add the kale. Cover and cook until the stalks of the kale are tender, about 20 minutes.
Serve with a generous sprinkle of pecorino Romano cheese.