Put broth in a large pan and heat until simmering. Add mushrooms, underside facing upward. Cover and cook for 5 minutes over medium/low heat.

Crack eggs and carefully pour each egg into a mushroom cap. Cover and continue cooking for approximately 5 minutes.

In a small pan add yogurt, lemon, mustard and egg yolk. Stir. Put pot over a larger pot of steaming water (double boiler). Stir while cooking over steam for 5 minutes.

Carefully remove mushroom/egg from pan and put on a plate. Spoon 1/4 cup of sauce over egg and top with dill and pepper!