Wash the cauliflower and broccoli and cut into small florets. Peel the potatoes and cut into quarters. Cook the potatoes in salted water for about 20 minutes. Blanch the cauliflower and broccoli in boiling salted water for about 10 minutes.
Cut the pork tenderloin into medallions. Let the oil get hot in a pan and fry the medallions well on all sides.
For the Bearnaise sauce, peel the shallot and cut into small cubes. Put the white wine vinegar with the white wine, the diced shallot, the pepper, the salt, as well as the chervil and the tarragon in a saucepan and bring everything to the boil. Then reduce everything to about halfway over a low heat. Then whip the sauce with the egg yolks thoroughly in a hot water bath. Melt the butter and add to the sauce and stir everything in again vigorously. Wash and chop the parsley and then add it to the sauce.
Grease four small baking dishes with oil and then first distribute the potatoes in them. Spread the vegetables over it. Place the fried medallions on top. Then spread the Bearnaise sauce over it and sprinkle with the cheese.
Gratinate in a preheated oven at 200 degrees for 5 minutes.