Remove the peel from the parsnips and celery. Boil parsnips in salted water until tender, then cut into slices or thick sticks.
Cut celery tuber into narrow slices on a bread slicer or possibly with a slicer. Blanch them briefly in salted water and dry on a kitchen towel. Sauté shallots in butter, place in a suitable bowl and cool.
Mix in spreadable sausage and parsley. Form a little of this mixture on each half of the celery slices and form a celery slice on top of each. Season each celery burger with pepper and a little salt, then pass through flour, beaten egg and finally breadcrumbs. In a frying pan with olive oil, finish the burgers.
Wrap the parsnip slices with Parma ham and bread them like the celery burgers. Bake in hot olive oil until done.