|Preheat the oven to 450˚F.
Split the squash in half; scoop out the seeds and white pulp. Pour the olive oil into your palm and rub the cut side of the squash, then place face down on a baking sheet. Roast until tender, about 40 minutes. Remove from the oven and allow to cool. This step can be done hours in advance.
While roasting squash, set a dry skillet over medium heat to toast walnuts for topping. Brown until fragrant. Chop once cooled.
Boil small amount of water for mushrooms. Place the dried porcini in a measuring cup and cover with 3/4 cup boiling water. Allow to steep while starting the sauce. If any porcini pieces are large, wait until they are tender from the hot water, then chop and return to the liquid.
In a large pot, boil water for gnocchi.
Melt butter in a large skillet. Mince the garlic. Sauté the garlic until it turns golden, then scoop the pulp from one half of the squash into the pan, avoiding the skin. Snip two of the sage leaves into ribbons and add to the squash. Add 1 teaspoon of salt and a few grinds of pepper, and stir to combine. Flatten any lumps in the squash using a fork. When the squash is heated and beginning to brown, add the porcini water, followed by the second half of the squash pulp. Cover and simmer until heated through and tender, about five minutes. Use the fork to press flat any remaining chunks of squash, so the sauce is reasonably smooth. Add more water if needed. Taste for salt, and correct as needed.
Add salt to boiling water. Cook gnocchi in boiling water until they float to the top, approximately 5 to 6 minutes. Toss gnocchi in saucepan with sauce for approximately 2 minutes on medium heat.
Top with walnuts and fresh grated cheese.