Preheat oven to 400°F. Coat a baking sheet with cooking spray. Cut squash in half lengthwise and scoop out seeds. Brush cut sides of the squash with oil and season with salt and pepper. Place the squash, cut-side down, on the prepared baking sheet, and roast until tender, 35 to 45 minutes.
To make pesto: With the motor running, drop garlic into a food processor or blender; process until finely chopped. Add parsley, sage, walnuts, salt and pepper; process until the herbs are finely chopped. Once again with the motor running, drizzle in broth and olive oil; process until the pesto has a creamy consistency, scraping down the sides of the workbowl once or twice.
When the squash is tender, spoon a teaspoon of the pesto into each squash half and serve, passing the remaining pesto separately.