Preheat the oven to 450 degrees F. Cut the bulbous end off the squash and reserve for another use. Remove the stem, then peel the remaining squash and cut in half crosswise. Using a spiralizer, shave the squash into ribbons.

Put the squash on a baking sheet and toss with the oil. Sprinkle generously with salt and pepper and roast until tender but still firm, 10 to 15 minutes.

Meanwhile, heat 1 tablespoon butter in a large skillet over medium heat until melted. Add the prosciutto in a single layer and cook until golden and curled around the edges, flipping with tongs halfway through, about 2 minutes per side. Transfer to a plate to cool, then coarsely crumble.

Add the remaining 5 tablespoons butter to the drippings in the skillet along with the sage leaves and a pinch of salt, and cook, stirring often, until the butter is a dark brown color, about 4 minutes. Remove from the heat.

Put the squash on a serving platter and drizzle with the butter and sage leaves. Top with the Parmesan and coarsely crumbled prosciutto. Serve immediately.