Preheat the oven to 400°F. Line a baking sheet with parchment paper.
Prepare the squash. Carefully cut the spaghetti squash in half lengthwise and scoop out the seeds and stringy center with a spoon.
Season. Brush the cut sides with 1 tablespoon of the extra-virgin olive oil and season with about half of the salt and several grinds of black pepper.
Roast. Place the squash halves cut-side down on the baking sheet. Roast for approximately 30–40 minutes, depending on the size of your squash. It's ready when the flesh is tender enough to separate easily into strands with a fork but isn't mushy.
Create the "spaghetti." Let the squash cool just enough to handle. Turn the halves over and use a fork to gently pull the flesh into spaghetti-like strands.
Finish. Drizzle the squash with the remaining tablespoon of EVOO. Add the Parmesan, remaining salt and freshly ground pepper and gently toss everything together.
Add the basil. Finish generously with fresh basil and, if you like a little heat, a pinch of red pepper flakes.
Serve directly in the squash halves for a simple but beautiful presentation.