Wash the fennel and carrots. Remove and set aside the fennel greens. Cut fennel tubers into thin slices and carrots into thin slices. Cook vegetables in salted water for 3-4 minutes until tender. Drain.
Cook the minced beef in a pan over medium heat without added fat for 5-7 minutes, stirring occasionally, until browned. Season with salt and pepper.
Make the béchamel sauce: heat clarified butter over medium heat, stir in flour for 1-2 minutes. Remove from heat, add stock and milk while stirring constantly. Return to medium heat and bring to a boil. Add half the cheese. Whisk egg yolk with 2 tablespoons of sauce in a small bowl, then stir this mixture back into the remaining sauce. Remove from heat. Season with salt, pepper, and a pinch of nutmeg.
Grease a baking dish with margarine. Layer alternately: vegetables, béchamel sauce, caraway seeds, and minced meat. Finish with a layer of béchamel sauce and sprinkle remaining cheese on top. Bake at 200°C (390°F) in a preheated oven for 30-40 minutes until golden and bubbling.
Sprinkle sunflower seeds and chopped fennel greens over the casserole.