Preheat the oven to 425°F. Line a baking sheet with aluminum foil.
Use a sharp knife to cut the squash in half then scoop out the seeds with a spoon. If using acorn or butternut squash, place the 2 halves, cut-side up, on the foil-lined baking sheet. If using delicata or kabocha squash, cut it into half-moons and arrange those on the foil-lined baking sheet. Brush the squash with 1 tablespoon of the olive oil, sprinkle with salt and pepper, and roast until soft (turn the delicata or kabocha squash once during roasting), about 20 to 25 minutes for the delicata or kabocha squash and 40 minutes for the acorn or butternut squash. Cool slightly. When cool enough to handle, cut the acorn or butternut squash into half-moon pieces.
Pour the balsamic vinegar into a small bowl. Add the remaining 4 tablespoons olive oil in a slow, steady stream, whisking constantly. Season to taste with salt and pepper.
Place the kale in a large bowl, add half the vinaigrette, and toss until evenly coated.
To assemble the salad, arrange the squash slices on a large platter – you can leave the skin on and people can cut it off themselves and drizzle with the remaining vinaigrette. Arrange the kale on top then sprinkle with pomegranate seeds, pine nuts, and shaved Parmesan