Clean and wash the broccoli and cut it into florets. Peel, wash and slice the kohlrabi. Blanch both together in boiling salted water for about 3 minutes. Put the frozen peas in a large sieve. Pour broccoli and kohlrabi in the sieve onto the peas, quench and drain. Clean, wash and cut the spring onions into long pieces. Arrange the prepared vegetables in a large casserole dish.
For the filling, select the spinach, wash and drain well. Puree the spinach and cream cheese briefly with a hand blender. Coarsely grate the mozzarella and stir into the spinach cream. Season with salt and pepper.
Cut fillets with skin from the bone, wash and pat dry. Cut a deep pocket into each chicken fillet. Season all around with salt and pepper. Distribute approx. 2⁄3 of the filling into the fillets. Mix the rest of the filling with cream, season to taste again if necessary. Pour sauce over the vegetables.
Preheat oven (electric cooker: 175 °C/circulating air: 150 °C/gas: see manufacturer). Heat oil in a large pan. Sauté the fillets in it, first on the skin side, then turn them over and fry them from the meat side. Place on the vegetables with the skin facing upwards. Roast in a hot oven for 35-40 minutes. Wash the chervil, shake dry and remove the leaves. Arrange meat and vegetables, sprinkle with chervil. Serve with young potatoes.