Bring a pot of salted water to a boil. In a skillet, melt 4 tablespoons of the butter. Add the sage and cook over moderate heat until crisp; with a slotted spoon, transfer to a small bowl. Add 1 more tablespoon of the butter to the skillet. Add the garlic and rosemary and cook until fragrant, 1 minute. Add the stock and boil until reduced to 1 cup, 8 minutes. Cover the skillet and remove from the heat.
Cook the noodles until al dente; drain. Return the noodles to the pot. Add the reduced stock and the remaining 3 tablespoons of butter and toss well. Stir in the 1/2 cup of grated cheese and season with salt and pepper. Transfer to a bowl, top with the toasted sage and remaining 2 tablespoons of grated cheese. Serve right away.