Melt butter with herbs de provence in a deep skillet. Add leek and cook covered until soft and crystal clear. Mix in heavy cream (start adding half the heavy cream) and correct seasoning.
Heat oil in a skillet and place mushroom slices in one layer (it is better to cook them in batches). Cook, without stirring until mushroom turns to a golden brown color. Turn mushrooms to the other side and cook for one minute more. Remove from the skillet and repeat procedure with the remaining mushrooms. Season and set aside.
Mix leek and mushrooms with warm rice. Add parmesan cheese and remaining heavy cream if necessary. Rice must be moist. Before serving stir in mozzarella cheese and mix thoroughly.
Serve immediately and sprinkle grated parmesan cheese and chopped parsley on top.