Remove the dark green part and the roots from the leeks, 800 g should remain. Wash the leek thoroughly, removing any sand residue between the leaves. Drain the leeks and cut diagonally every 2 cm. Cook in boiling salted water for 15 minutes, drain and drain on a cloth.
In the meantime, for the cheese sauce, put the cream with mascarpone in an appropriately large saucepan, heat and stir until smooth. Add the Gruyère and let it melt while stirring, season with salt and pepper. Put aside.
Mix the flour with the paprika powder in a bowl and roll the leek sticks in it. Melt the butter in a large pan and fry the leek sticks until golden. Grease a gratin dish with butter and insert the leek sticks. Cut the ham into 1 cm wide strips and spread over them. Pour the cheese sauce over them.
Bake at 200 ° C in a preheated oven for 20 minutes. Wash the parsley, spin dry and chop finely. Sprinkle over the leek gratin and serve immediately.