Make the brown butter. Heat a stick of butter over medium-low heat for 8 to 10 minutes. As the butter cooks, the solids will sink to the bottom and begin to brown. Watch it carefully so you don’t burn the solids. Strain through a cheesecloth lined sieve or a coffee filter and set aside. You will use half for this recipe; cover and refrigerate the rest for another day.
Peel and chop the squash, mince the garlic, slice the shallots, and chop the sage.
Preheat the oven to 400°. Toss the squash with 1 tablespoon of oil, the garlic, ½ tablespoon of the sage, and salt and pepper. Roast until tender, about 20 minutes. Set aside.
Bring a large pot of water to boil and salt it. Drop in the penne and cook until tender, about 10 minutes.
Heat the remaining oil in a large sauté pan and add the shallots, 1/3 teaspoon salt, and a pinch of pepper. Cook over medium heat until the shallots begin to soften, about 3 minutes. Add the wine and cook until the pan is nearly dry, about 3 minutes.
Just before draining the pasta, add a cup of the pasta water to the shallots, along with the squash, a quarter cup of the brown butter, ¼ teaspoon salt, and a pinch of pepper. Drain the pasta and add it to the pan. Cook over medium heat for 1 or 2 minutes.
Toss in the walnuts and the rest of the sage and season to taste with salt and pepper. Serve with freshly grated parmesan.