Peel the potatoes and carrots and cut into small cubes. Cut the savory into strips. Cook the vegetables and diced potatoes in a large saucepan with salted water for five minutes, add the pizzoccheri and continue cooking for 12-15 minutes.
Drain the pizzoccheri and vegetables well, arrange in a bowl and mix in the thinly sliced cheese. Spread the grated parmesan over the dish.
Toast the garlic and some sage leaves in hot butter and burn the pizzoccheri with it. Serve very hot.