Wash pork fillets, dab dry and brush with 3 tbsp vinegar. Cover and chill for about 30 minutes, wash thyme, shake dry and remove the leaves.
Roast pine nuts in a pan without fat, remove from the pan immediately and let them cool down. Clean and wash the carrots, leaving a little green. Peel, wash and coarsely grate the potatoes. Mix in starch, parmesan cheese and egg, season with salt and pepper.
Heat 20 g clarified butter in a frying pan. Dab the fillets dry and fry them in the hot lard all around. Season with salt and pepper and deglaze with 3 tbsp vinegar and honey. Sprinkle with 3/4 of the thyme and turn in the frying stock.
Pour on the stock, bring to the boil briefly and cook in the preheated oven (electric cooker: 150 °C/ circulating air: 125 °C/ gas: see manufacturer) for approx. 20 minutes.
Covered carrots and stew them in little boiling salted water for about 10 minutes. Heat approx. 15 g clarified butter in a large pan. Using a tablespoon, add 4-5 heaps of the potato mixture to the pan, flatten them a little and fry them until golden brown, turning them over.
Drain the finished potato cookies on kitchen paper and keep warm. Bake about 20 small potato cookies in portions.
Take the finished pork tenderloin out of the oven and let it rest in the stew for about 5 minutes. Drain the carrots. Wash tarragon, dab dry and chop coarsely. Heat the fat in the pot, carefully toss in the carrots, pine nuts and tarragon.
Cut the pork fillets into slices and sprinkle with the remaining thyme. Arrange fillet, tarragon carrots and potato cookies on a large plate. Drizzle meat with balsamic frying stock.
Add the remaining stock.