Peel the celeriac and cut into large pieces, sauté briefly in butter over low heat, season with salt and pepper, add the whipping cream and cook gently in a closed saucepan until the celeriac is very soft – this takes about half an hour. You may need to add a little water in between, but always as little as possible.
In the meantime, clean and rinse the celery stalks, then cut them into sticks 5 cm long and half a centimeter thick or wide. Blanch these sticks briefly in plenty of boiling hot salted water for 3 minutes and then rinse with cold water.
When the celeriac is cooked, purée it with the liquid in the saucepan, cool the purée a little bit and then stir in the eggs. Fill the mixture into a suitable buttered dish, not much bigger than the puree, put it into a gratin dish with hot water and cook the celery flan for about 45 minutes in a heated oven at 180 degrees.
Just before the end of the cooking time, sauté the celery sticks in a little olive oil, season with salt and pepper and sauté them at a low temperature for 5 minutes, they should be semi-soft, i.e. still have bite.
Remove the celery flan from the pan, cut 4 thick slices and place them on the plate already covered with celery.