Slice the parsley roots into long, paper-thin slices using a mandoline and place them in ice-cold water for 15 minutes. Spin them dry in a salad spinner.
Heat the oil to approx. 180 degrees in a pan – the oil is ready when it sizzles around a wooden toothpick. Add the parsley root slices in two batches and fry them until golden and crisp; remove them with a slotted spoon or frying spoon and leave them to drain on kitchen paper. Season with fine salt.
Scrub the parsnips clean with a stiff brush and place them on a sheet of baking paper along with a clove of crushed garlic. Melt 25 g of butter, pour it over the parsnips and garlic, and season with salt and pepper. Give everything a good toss, fold the baking paper over the parsley roots and bake them in the oven for approx. 35–40 minutes, until tender.
Remove them from the oven and leave them to cool slightly until they are warm. Cut them in half lengthways and fry the parsley roots in a pan in the remaining butter until they are golden. Leave them to cool slightly before serving.
Rinse the parsley thoroughly, pluck the leaves and dry them in a salad spinner or a tea towel. Place the parsley leaves and garlic in a blender with 100 ml of the oil and blend for a couple of minutes, until the oil is green and has a smooth consistency. If you want the mayonnaise to be completely smooth, pass the oil through a fine-mesh sieve. Now mix the parsley oil with the rest of the oil.
Place the egg yolks in a large bowl together with the mustard, a little salt, freshly ground pepper and 2 tbsp lemon juice, and whisk well with an electric whisk, or if you have a good balloon whisk to make the mayonnaise. Now whisk the herb oil into the egg yolks a little at a time in a thin stream. Pour slowly so that the oil is constantly being whisked into the egg yolks. Pause occasionally whilst adding the oil and whisk the mayonnaise thoroughly. Continue until all the oil has been added, then whisk thoroughly once more.
Finally, season to taste with salt and, if desired, extra lemon juice; the dill mayonnaise tastes best if it is slightly on the tart side. Transfer the herb mayonnaise to a piping bag. Refrigerate the mayonnaise immediately, where it will keep for 5–6 days.
Spread butter on the rye bread and arrange the warm parsley roots on top, then dot small dollops of parsley mayonnaise around the roots. Next, add the pickled onions, deep-fried parsley roots and small fresh parsley leaves.
