1. Preheat oven to 425°.
2. Place squash on a jelly-roll pan coated with cooking spray. Bake at 425° for 25 minutes.
3. Bring stock and 1 cup water to a simmer in a saucepan. Keep warm.
4. Heat a large saucepan over medium-high heat. Add oil to pan. Add onion, salt, and pepper; cook 4 minutes. Add barley and garlic; cook 2 minutes. Stir in 1/2 cup stock mixture; cook 4 minutes, stirring frequently. Reduce heat to medium-low. Reserve 1/4 cup stock. Add remaining stock, 1/2 cup at a time, stirring frequently until each portion is absorbed. Remove from heat. Stir in reserved 1/4 cup stock and 1 ounce cheese. Fold in squash. Sprinkle with remaining cheese and sage.