Peel the asparagus, cut off the woody ends and cut the asparagus into three at an angle. Cook in plenty of boiling water with a little salt and sugar for 8-10 minutes and remove from the water. Keep the asparagus stock. Peel and wash the carrots and potatoes. Cut carrots diagonally into slices, cut potatoes into slices.
Cook the potatoes in boiling salted water for about 12 minutes, after 8 minutes add the carrots and cook them. Drain and quench. Fry chicken fillets in hot oil on both sides for 5-6 minutes at medium heat until golden brown, season with salt and pepper. Melt the fat in a saucepan, stir in the flour. Add 500 ml asparagus stock while stirring vigorously, bring to the boil and cook over low heat for 4 minutes. Grate the gouda and cut the gorgonzola into cubes. Stir half the gouda and gorgonzola into the sauce. Layer asparagus, potatoes and carrots in a greased casserole dish. Cut the chicken fillets into slices and place them on the vegetables.
Grate the gouda and cut the gorgonzola into cubes. Stir half the gouda and gorgonzola into the sauce. Layer asparagus, potatoes and carrots in a greased casserole dish. Cut the chicken fillets into slices and place them on the vegetables. Pour the sauce over them and sprinkle with the remaining cheese. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for approx. 20 minutes