Preheat the grill to high. Trim the chicory and cut lengthways into quarters. Heat the olive oil in a shallow pan over a moderate heat and soften the shallot for 2 minutes. Add the chicory quarters, cut side down, and cook for 3 minutes. Turn them over, cover the pan and cook for another 3 minutes, then season with salt and pepper.
Slice the cheese, arrange the pieces over the chicory and sprinkle the oregano on top. Slide under the hot grill for a few minutes until the cheese is bubbling. Serve immediately.