Preheat oven to 400ºF. Place the squash halves on a rimmed baking sheet. Brush the cut side of each squash half with 1 Tbsp. olive oil, and season with salt and pepper.
In a medium bowl, combine tomatoes, pesto, garlic, chili flakes, remaining 2 Tbsp. olive oil, and a pinch of salt.Place a wedge of feta cheese inside each squash half, followed by the tomato-pesto mixture, divided equally between each half.
Bake until the squash flesh is tender and the tomatoes burst, about 55 minutes. Use a fork to scrape the squash strands into the feta and tomato mixture, and continue mixing until everything is combined. (If your squash boats are overflowing and it's hard to mix, transfer everything to a large bowl to mix, and then place back into squash boat.) Garnish with fresh basil and extra cracked black pepper.
