Position oven rack in middle; 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 and black pepper. Place 2 cups spinach, 1 ½ tablespoons basil, 1 tablespoon garlic and ½ teaspoon oregano in each squash half; top each with a feta piece. Drizzle each with 1 ½ teaspoons oil. Bake until the squash flesh is tender and the feta is lightly browned, about 45 minutes.
Using a fork and tongs, scrape the feta-spinach mixture and the long strands of squash flesh into a large bowl. Add water, salt and the remaining 2 tablespoons oil; stir to combine. Return the mixture to the squash shells; cut each in half widthwise. Transfer each piece to a plate; drizzle with balsamic glaze. Garnish with basil, if desired. Additional reporting by Carrie Myers, M.S. and Linda Frahm
