Cook the chopped pancetta (or bacon) in 2 tablespoons of butter in a large saute pan over medium heat. Stir often until it begins to crisp and brown on the edges.
Add onion and garlic and cook for 2 to 3 more minutes while stirring until the onion begins to soften.
Add chopped chestnuts and all but a small handful of apples to the pan along with the water. Let simmer while stirring until liquid reduces by about half.
Turn off heat and stir in Parmesan.
In a separate small skillet, melt the remaining 4 tablespoons butter over medium heat. Add the sage leaves to the pan and cook while stirring until they begin to darken in color and become crispy, and the butter browns. Immediately remove from heat. This sauce can overcook easily so sometimes I even immediately remove it from the pan so it doesn't keep cooking.
Divide the cooked pasta among 4 or 5 plates, then top with the chestnut and apple mixture and the sage brown butter sauce. Garnish with extra grated Parmesan and diced green apples and serve.