Put the pine nuts in a small skillet over low heat and slowly toast them, stirring, until they're golden brown and fragrant, about 2 minutes. Set aside off heat.
To prepare the butternut squash, cut off the top and bottom, then use a sharp knife or vegetable peeler to remove the hard skin. Cut the squash in half lengthwise and remove the seeds with a spoon. Slice the squash into sticks and then slice the sticks into cubes.
Meanwhile, melt the butter in a small skillet or saucepan over low heat. Skim off as much of the foam as you can. Put the squash in a bowl and pour in the melted butter. Sprinkle with salt and pepper and toss to combine.
Spread the squash out on a rimmed baking sheet and roast, shaking the baking sheet once or twice during roasting, 25 to 30 minutes. Crank up the heat to 400 degrees F and roast until the squash is sizzling and golden brown around the edges, another 15 minutes or so. Set aside to cool for 5 minutes, then add the Parmesan and toss together. Toss in the pine nuts.
Mix the olive oil with the balsamic in a bowl and sprinkle in a little salt and pepper. Put the salad greens in a serving bowl and toss with half the dressing. Add the squash mixture and lightly toss it in. Serve the extra dressing on the side. Top with additional Parmesan if desired.