For the sauce, clean or peel the vegetables, wash and chop them coarsely. Wash the thyme. Heat butter in a pot. Brown vegetables and thyme in it. Dust with flour and sweat lightly. Add stock and cream while stirring, bring to the boil and reduce by half.
Remove thyme stalks. Finely puree the sauce with a hand blender. Season to taste with salt, pepper and lemon juice. Pass through a fine sieve. Wash the chives, shake dry, cut into small rolls and stir into the sauce.
Wash the beans and cut off the ends. Cover and simmer in salt water for about 2 minutes. Lift out and rinse in cold water.
Whisk 2 eggs in a bowl. First turn the beans in flour, then pull them through the eggs and bread them in breadcrumbs. Heat 2-3 tbsp. lard in a large pan. Fry the beans for 2-3 minutes on both sides until crispy.
Season with salt.
Heat 2 tablespoons of lard in a second pan. Fry 4 fried eggs in it. Arrange on the cutlet beans. Add chive sauce.