Heat the butter and 1 tablespoon of the oil in a large saucepan over medium heat. Add the onion and cook for 5 minutes. Add the rice and cook, stirring constantly, for 2 minutes. Reduce heat to medium-low. Add the wine and cook, stirring frequently, until the liquid is absorbed. Add the broth, 1/2 cup at a time, stirring occasionally and waiting until it’s absorbed before adding more. This should take about 30 minutes. The rice should be tender but still slightly firm.
Meanwhile, about 5 minutes before the risotto is done, heat 2 tablespoons of the remaining oil in a large skillet over medium heat. Add the radicchio and garlic and cook, stirring occasionally, until the radicchio is browned and slightly wilted, about 5 minutes. Add the oregano (if using), vinegar, and 1/4 teaspoon of the salt. Transfer to a plate.
Remove the risotto from heat and stir in the Parmesan, the remaining salt, and the pepper. Cover to keep warm.
Wipe out skillet, return to medium heat, and heat the remaining oil. Add the bread crumbs and cook until golden brown, 2 to 3 minutes. Remove from heat. Spoon the risotto into individual bowls and top with the radicchio and bread crumbs.