Step 1Heat the oven to 400 degrees and toast the walnut halves in a dry pan in the oven until lightly browned and nutty smelling, about 8 to 10 minutes. Chop coarsely and set aside.
Step 2Pour the oil into a small saucepan to a depth of about 1 inch and place over high heat. When the oil reaches 375 degrees, add the sage leaves and fry just until they darken slightly and turn crisp, only a couple of seconds. Remove the leaves with a slotted spoon and drain on paper towels.
Step 3Combine the chicken or vegetable stock and 4 cups water in a large saucepan and bring to boil, then reduce the heat to maintain a bare simmer.
Step 4In a large skillet, place 3 tablespoons of butter and the onion over medium-high heat and cook, stirring, until the onion begins to soften, about 3 minutes. Add the squash and cook until it is shiny and beginning to soften, about 5 minutes. Add the wine and cook until it reduces to a syrup, about 3 minutes.
Step 5Add the rice to the pan and cook, stirring, until the mixture is dry enough that the rice makes a "singing" sound as it scrapes the bottom. Add 1 cup of simmering stock and the salt to the pan and stir it in. Cook until the rice absorbs enough liquid that you can see dry pan when you stir, about 5 minutes. Repeat, adding more stock each time, until the rice is firm but tender, with no chalky center; reserve the last one-half cup of the stock. This will take about 20 minutes in all. You don't need to stir continuously, just when you add the stock to the pan and when it is nearly dry.
Step 6When the rice is done, add the reserved stock to loosen the mixture slightly and remove the pan from the heat. Stir in the remaining 2 tablespoons of butter and the one-fourth cup of grated Parmesan cheese. Stir vigorously in order to free as much starch as possible, which in combination with the cheese will thicken the mixture slightly.
Step 7Spoon the risotto in generous mounds in the center of heated flat bowls. Scatter the toasted walnuts over the top and place the fried sage leaves on top of that, 3 or 4 to the bowl. Serve immediately, passing additional cheese for those who want it.