Wash the asparagus and cut off the woody ends generously. Wash the meat and pat dry.
Heat 1 tablespoon of oil in a large coated frying pan. Fry the fillets on each side for about 6 minutes at medium heat. Season with salt and pepper. Heat 1 tablespoon of oil in a saucepan or a second pan.
Fry the asparagus for 8-10 minutes while turning. Season with salt.
Meanwhile wash tarragon. Pluck off the leaves and chop them roughly. Peel and finely dice the shallot. Take the chicken out and keep it warm. Sauté shallot in hot frying fat. Briefly sauté the flour.
Stir in 1/8 l water, milk and stock, bring to the boil. Add half tarragon, simmer for 2-3 minutes.
Puree the sauce. Season to taste with salt, pepper and lemon juice. Season asparagus with salt. Serve with chicken filet and sauce. Cut baguette into slices and serve with it.