Clean and wash the carrots and cut them into slices at an angle. Clean, wash and cut the celery into pieces. Wash potatoes thoroughly and cook in boiling salted water for about 18 minutes.
Steam carrots in little boiling salted water and 1 teaspoon of fat for about 15 minutes in a closed pot. After 5 minutes add the celery and cook it. In the meantime, heat the remaining fat in a pot, sauté the flour in it until golden brown and deglaze with milk and stock.
Add cheese and stir in the sauce until creamy. Season to taste with salt and pepper. Wash the parsley, dab dry and pluck the leaves from the stalks. Drain the potatoes, rinse and peel.
Drain off the vegetable water (a small residue remains) and stir in the sauce. Cover vegetables with some sauce and arrange with some potatoes. Garnish with parsley leaves. Sprinkle with pepper to taste.
Add the remaining vegetables and potatoes.