Place yucca in a saucepan, cover with water and bring to a boil. Cook yucca until tender and soft.
Remove yucca from saucepan and place it in a bowl. Mash it with a potato masher until smooth and transfer it to mixer. Mix yucca puree at low speed with the hook or paddle attachment. Add butter and milk, gradually, while beating. Continue beating until a soft puree is obtained. Add both cheeses and egg yolks. Season to taste.
Melt butter in a large skillet and sauté sliced mushrooms. Combine with yucca puree. Correct seasoning.
Transfer puree to a greased ovenproof serving dish. Sprinkle Mozzarella cheese on top.
Bake in preheated oven 180°F (350°C) until hot and serve.