Bring the stock to a boil, then lower to minimum heat and keep it so throughout the recipe in order to be adding it warm.
Mince the shallot and set aside. Halve the radicchio lengthways, place it with the cut facing down, and slice into 1 cm strips. Push the sausage meat out of the casing and gently crumble it.
Set a heavy duty skillet (or Dutch oven) on medium heat and melt half of the butter. Add the shallot to the butter and cook on medium heat for a couple of minutes, until soft. Add the crumbled sausage and cook for 10 minutes, stirring often.
Add the rice and toast stirring continuously until it becomes slightly translucent, another couple of minutes. Pour in the wine and stir constantly until it evaporates, then stir in the radicchio.
Add the stock in batches, always adding just enough to cover the rice. Simmer on medium heat stirring from time to time to prevent it from sticking to the bottom of the skillet. Only add more stock when the previous batch has been absorbed. Proceed until all of the broth has been added or until the rice is cooked through. It should take up to 20 minutes.
After the last addition, just before all of the broth has ben absorbed and the texture is still soupy, remove from the heat. Fold in the remaining butter and grated cheese.