Soak the borlotti beans overnight. In the morning, drain the beans and place them in a medium-sized soup pan.
In a 12 to 14-inch saucepan, heat the oil over a medium-high flame until hot but not smoking. Add the onion and sweat over medium heat until soft and translucent, about 5 minutes. Add the carrot and celery.
Meanwhile, slice the sausage into half moons. Add the beans, sausage and the rice to the saucepan. Using a wooden spoon, gently mix the rice in with the sausage and onion, so that the grains are coated in the olive oil, and the sausage is lightly browned.
Add the cabbage and tomatoes, and stir to combine. Add the chicken stock, bring to a boil and reduce to a simmer. Let simmer gently until the rice is cooked and the vegetables tender, about 45 minutes to 1 1/2 hours for a thicker texture. Season, to taste, with salt and pepper. Serve with Parmigiano-Reggiano, for grating.