In an 8- to 12-quart pot, bring 6 quarts (24 cups) salted water to a rolling boil.
In a large nonstick skillet, heat 2 tablespoons of the olive oil over medium-high heat until hot but not smoking. Add the sausage and cook, breaking it up with a wooden spoon, until browned but not yet crispy. Remove the meat from the skillet with a slotted spoon and set aside.
Add the onions and remaining tablespoon of olive oil to the skillet and saute until the onions are soft. Add the sausage back along with a pinch of red pepper flakes and saute an additional minute. Reduce the flame to medium low and pour in the wine, cooking until it is reduced by half, 3 to 4 minutes. Remove the sauce from the heat.
Add the pasta to the boiling water and cook until al dente. Drain the pasta and add it to the sauce in the skillet. Add the Parmigiano-Reggiano and radicchio and toss to combine the ingredients. Garnish with the crushed walnuts, a drop of extra-virgin olive oil and a light dusting of freshly grated Parmigiano-Reggiano.