Saute the onions and thyme with the butter for 20 minutes. Add salt and pepper. Beat the egg with the cream, adding in the parmigiano, onion and the rest of the ingredients. Roll out the pastry dough, add it to the pan, pricking the bottom.
Cut the radicchio into a fine julienne, then pour the onion mixture over it. Bake the quiche in the oven at 190° for 20 minutes, then lower the temperature to 170°, cooking for another 20 minutes.
When the quiche is baked, let it rest for at least 12 hours before serving, then finish with a drop of balsamic vinegar from Modena.