Heat oven to 425˚F. Cut the squash in half, lengthwise, and remove the seeds. Once the seeds are removed, slice each half into ¼” thick pieces—place on a sheet tray along with two teaspoons olive oil and salt. Toss to coat and combine then place in the oven.
In a small bowl, combine the scallions with the remaining ½ teaspoon of olive oil. Roast the squash for 15 minutes then sprinkle the scallions on top. Return to the tray oven and roast for another 10 to 15 minutes, until squash is starting to brown and is tender.
While the squash is roasting, cook the pasta until tender in a pot of salted water. Drain and return the pasta to the pot. Add the melted butter, parmesan, and lemon zest. Stir to coat and melt the cheese.
Once the squash is done, combine the pasta with the arugula, squash, and walnuts. Add more arugula if desired- this dish is meant to be more salad feeling, less pasta. Top with chili flakes and more parmesan if desired.