Preheat the oven to 400°F. Line a large, rimmed baking sheet with parchment paper.
Cut the spaghetti squash in half lengthwise: Using a very sharp, sturdy chef's knife, trim off the base end of the spaghetti squash so you have a flat surface. Stand it upright and carefully cut it in half lengthwise from top to bottom. Scoop out the seeds and stringy insides.
Place the halves cut-side up on the parchment. Drizzle each with 1/2 teaspoon oil and sprinkle with the salt and pepper. Rub lightly to evenly coat the insides of the squash.
Slice the block of feta in half, and place one half in each squash cavity.
In a small bowl, stir together the tomatoes, pesto, garlic, and remaining 2 teaspoons oil. Spoon over the feta.
Bake the squash until the tomatoes are breaking down and the squash is fork-tender and its skin gives a little when pressed on the outside (be careful, it is hot!), about 55 minutes to 1 hour 5 minutes, depending upon your squash.
With a fork, fluff the squash flesh inward to separate the strands and stir together with the feta and tomatoes (the feta will be nice and melty). Sprinkle with fresh basil.
Notes
TO REHEAT: Rewarm leftovers in an oven at 350°F until hot and melty.