Preheat the oven to 400°F (200°C).
Carefully slice the spaghetti squash lengthwise into two halves. Scoop out and discard the seeds with a spoon.
Arrange both squash halves with their cut surfaces facing upward in a baking dish or on a rimmed baking sheet. Drizzle the flesh with 1 tablespoon of the olive oil, then season evenly with ¼ teaspoon kosher salt and a pinch of black pepper. Spread the oil and seasonings over the exposed flesh using clean hands or a pastry brush.
Measure out half of the total feta cheese, approximately 2–4 ounces depending on the amount being used, and divide it between the centers of the two squash halves. Gently press the feta pieces into the squash so they can soften and melt as the squash roasts. Reserve the remaining feta.
In a small bowl, combine the cherry tomatoes, chopped roasted red peppers, minced garlic, Italian seasoning, and the remaining 2 tablespoons olive oil. Add kosher salt to taste along with a pinch of ground black pepper, then stir until everything is evenly coated.
Divide the tomato and roasted pepper mixture evenly between the prepared squash halves, arranging it over the feta.
Transfer the filled squash halves to the preheated oven. Roast for 50–60 minutes, or until the spaghetti squash is tender when pierced with a fork and the tomato-feta filling is hot and bubbling.
Remove the squash from the oven and allow it to cool for at least 10 minutes, making the shells easier to handle.
Use a fork to gently scrape the softened squash flesh into spaghetti-like strands. Mix the strands directly with the roasted tomato and feta filling until the melted cheese is thoroughly incorporated and the mixture develops a creamy consistency.
Spoon the combined spaghetti squash mixture back into the hollowed squash shells to form filled squash boats.
Finish with chopped fresh basil and additional or reserved feta cheese, if desired. Serve the baked feta spaghetti squash while warm.