Put the cabbage and potato into a pan, add water to cover, and season with salt and pepper. Bring to a boil, then lower the heat, and simmer for 20 minutes until the cabbage is tender and the potato is almost disintegrating.
Divide the butter between three small pans and cook the onion, garlic, and sage in the separate pans until soft and golden brown.
Roll out the pasta dough into a fairly thick sheet on a lightly floured counter and cut into 1/2-inch wide ribbons about 8 inches long.
Add the pizzoccheri to the pan of cabbage and potato, cook for 5 minutes, then drain, and transfer the mixture to a large dish. Pour the three hot butters over the mixture and toss lightly.
Arrange a layer of pizzoccheri-vegetable mixture on the base of a soup tureen, place a layer of cheese slices on top, and sprinkle with the Parmesan. Continue making alternating layers until all the ingredients are used. Serve hot.