Clean the asparagus and cut off the woody ends. Peel and wash the carrots and cut them into long sticks. Cook the asparagus and carrots for about 5 minutes each in boiling salted water. Remove and rinse in cold water.
Dab asparagus and carrots dry, spread on the ham and roll in it. Place the packet in a greased baking dish, sprinkle with pepper and spread Sauce Béarnaise on top. Bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for approx. 10 minutes.
The last 3 minutes put the oven on grill to gratinate the sauce. Wash and finely chop the parsley. Remove the dish from the oven and sprinkle parsley on the parcels.