Place yucca pieces in a large saucepan, cover with water, add salt and cook over medium heat until soft and tender. Remove from heat and drain yucca. Heat milk in a medium saucepan with 1/3 cup butter. Force hot yucca pieces through a strainer into hot milk stirring to form a puree. Add parmesan cheese, mix well and season with salt and pepper. Fold in eggs.
Melt remaining butter and brush sides and bottom of a soufflé dish (8 cups capacity). Coat sides and bottom with half of the dry bread crumbs.
Spoon half of yucca puree into prepared soufflé dish. Combine swiss cheese and mozzarella cheese and cover puree. Spoon remaining puree.
Combine remaining dry crumbs with fresh bread crumbs, chopped parsley and grated parmesan cheese and sprinkle on top.
Bake in preheated oven to 350ºF (180ºC) for 35 minutes. Increase the temperature to 425ºF (180ºC) and continue baking for 15 to 20 minutes more until soufflé is hot and the top part is golden. This soufflé can be prepared without baking 1 day ahead and kept covered in the refrigerator. Bring to room temperature before baking.