Heat a small sauté pan over medium heat. Add pieces of prosciutto and allow it to crisp up, about 2-3 minutes on each side. Remove prosciutto from the pan and set aside.
Add one teaspoon of butter or oil to the pan and add 5-6 whole sage leaves. Allow sage leaves to crisp, about 3 minutes on each side. Remove sage leaves and drain on paper towel.
Cook pappardelle according to package instructions in well salted water. Reserve 1/4 cup of pasta cooking water.
In a large sauté pan over medium heat, add one tablespoon of the butter. Add the pumpkin and shallots and cook, stirring frequently, until the shallots are soft and pumpkin begins to crisp, approximately 5 minutes.
Next, reduce the heat to medium-low and add the rest of the butter, thyme, chopped sage and walnuts. Allow butter to melt and then continuously swirl pan until walnuts are toasted and the butter is browned and has a nutty aroma, which will take approximately 5-8 minutes.
Turn off the heat, add pappardelle and crispy prosciutto and toss so everything is coated in the brown butter. Taste and add salt and pepper, as needed, as well as pasta cooking water, to thin the sauce.
Pour pasta into serving bowl and top with crispy sage.