Cut each head of radicchio in half lengthwise, then cut each half into 4 wedges. (Leave the cores intact; they'll help hold the wedges together.) Set aside.
In a small bowl, whisk together the vinegar, garlic, salt, pepper, anchovies (if using), and 3 tablespoons of the oil; set aside.
Heat the remaining oil in a large skillet over medium heat. Add the radicchio in a single layer and cook for 3 minutes. Turn the radicchio, add the vinaigrette and oregano, and cook until the radicchio is tender and slightly browned, about 3 minutes more. Serve warm or at room temperature.