Bring a large pot (about 6 cups of water to a boil. Salt and add the cabbage. Cook cabbage until wilted, tender, and bright green, about 5 to 7 minutes. Remove and add potatoes, cook for about 8 to 10 minutes until fork-tender. Set the cabbage and potatoes aside.
Drain water and fill pot with another 6 cups. Bring water to a boil. Add salt and pizzocheri, stirring often until al dente and toothsome, about 6 to 8 minutes.
In a medium skillet over medium heat, melt butter and cook until it begins to turn a golden brown, about 1 minute. The milk solids will separate at this point creating tiny golden brown specks. Add olive oil and stir. Add garlic and cook stirring until the butter begins to foam and the garlic is golden brown, about 2 to 3 minutes.
Add sage, being careful of splatter. Cook for a few seconds until it wilts and crisps up slightly. Add the cabbage and potatoes and toss to coat in the butter sauce. Then, gently fold in the pizzocheri and fontina. Season with salt to taste.
Serve with lots of grated parmigiano cheese.