Prepare the oven and squash. Preheat the oven to 400°F (200°C). Cover a baking sheet with parchment paper. Slice the spaghetti squash lengthwise, scoop out the seeds, and discard them. Arrange both squash halves on the lined baking sheet with the cut surfaces facing upward.
Assemble the filling. Divide the 8-ounce feta block into two equal portions and position one piece in the hollow center of each squash half. Distribute the halved cherry tomatoes around the feta, then scatter the minced garlic over the top.
Season the squash. Drizzle the 4 tablespoons of olive oil evenly over the feta, tomatoes, and squash. Season generously with salt and black pepper. Lightly press some of the tomatoes to encourage their juices to release.
Bake until tender. Place the baking sheet in the preheated oven and roast for approximately 45–50 minutes. The squash is ready when its flesh can be pierced easily with a fork and the feta has softened, with lightly golden edges.
Shred and combine. Remove the baked squash from the oven. Using a fork, scrape through the softened flesh to create spaghetti-like strands. Continue raking and stirring so the squash strands become thoroughly combined with the roasted feta, tomatoes, garlic, and their juices.
Finish with basil. Sprinkle the 1/4 cup of freshly chopped basil over the mixed squash. Serve immediately.