In a wide saucepan, fry the bacon over moderate heat until just crisp on the outside, but not overcooked. Remove the bacon bits with a slotted spoon and drain on paper towels.
Wipe excess bacon fat from the pan add the radicchio, seasoning it lightly with salt and pepper. Cover, and cook, stirring a few times while it’s cooking, until wilted, about 5 minutes. Remove from heat, uncover, and let come to room temperature. Once cool enough to handle, chop the radicchio into bite-size pieces, and set aside.
Heat the stock in a saucepan and keep it warm while you make the risotto.
Melt the 2 tablespoons of butter in the wide saucepan and add the shallots. Cook, stirring constantly until translucent. Add the rice and cook another minute, stirring. Add the wine and continue to cook until the wine is completely absorbed by the rice.
Using a ladle, add enough of the warm stock to cover the rice, enough so there is about 1/4-inch (1cm) liquid above the rice. Continue to cook at a gentle simmer, stirring frequently, adding more warm stock as you go, making sure there is no more than 1/2-inch (1cm) of liquid on the surface.
When you’ve added almost all but the last few ladlesful of the stock, stir in the thyme, bacon, and radicchio. Continue cooking, adding the rest of the stock (and the chicken or duck, if using), until all the liquid has been added. It’s done when you taste a few grains of rice, and they are cooked through. If not, continue cooking, adding a bit of hot water or more stock if you have it, until it’s the right consistency.
Stir in the additional tablespoon of butter and the grated cheese. Remove the risotto from the heat, cover, and let stand a few minutes before serving. Serve in warm bowls, with additional grated cheese on top.