Position rack in middle of oven; preheat to 400°F. Line a large rimmed baking sheet with parchment paper or foil.
Place squash halves, cut-sides up, on the prepared baking sheet. Drizzle with 1 tablespoon oil; sprinkle with crushed red pepper, pepper and salt. Place 1 feta piece, ¾ cup tomatoes, 1½ tablespoons basil, 1½ teaspoons garlic and ¾ teaspoon oregano in each squash half. Drizzle each with 1½ teaspoons oil. Bake until the squash flesh is tender and the tomatoes burst, 50 to 55 minutes.
Remove from oven. Using a fork and tongs, scrape the squash contents and the long strands of squash flesh into a medium bowl. Drizzle in the remaining 1 tablespoon oil; stir to combine. Return the mixture to the squash shells; cut each in half widthwise. Transfer each to a plate; drizzle evenly with balsamic glaze and serve.
