Step 1Heat the oven to 400 degrees. Cut the butternut squash lengthwise into quarters, then seed and remove any of the stringy center. Cut the pieces crosswise into slices a little thicker than one-fourth inch. Place the squash in a large mixing bowl and add 2 tablespoons olive oil, the garlic, the thyme and 1 teaspoon salt. Toss to coat well. Add the Parmigiano-Reggiano and toss again.
Step 2Line a jellyroll pan with metal foil and arrange the squash wedges in a single layer. Roast until the squash is tender, fragrant and lightly browned, about 20 minutes. Remove from the oven and set aside to cool.
Step 3Remove and discard the stems from the kale. Chop the leaves into bite-sized pieces. Place in a large mixing bowl with 1 teaspoon salt and 1 tablespoon olive oil. Grab the leaves by the handfuls and massage them roughly. Don't be timid. After a minute or two, the coarse, stiff leaves will turn soft and silky. You'll have about half the volume of kale you started with. Add the sherry vinegar and toss well. Season to taste with more salt and vinegar if necessary.
Step 4Arrange the greens in a low mound on individual serving plates or on a platter. Scatter the cooled squash pieces over the top. Sprinkle with chopped walnuts and serve.