Step 1

Adjust oven racks to upper-middle and lower-middle positions and heat oven to 400 degrees. Line rimmed baking sheet with aluminum foil and spray with vegetable oil spray.

Step 2

Brush cut sides of squash with 1 tablespoon oil, season with salt and pepper, and lay, cut side down, on prepared sheet. Roast on lower rack until tender and tip of paring knife inserted into flesh meets no resistance, 45 to 55 minutes. Remove squash from oven and increase oven temperature to 450 degrees.

Step 3

Meanwhile, bring 2 cups water to boil in small saucepan. Stir in barley and ¼ teaspoon salt and cook until barley is tender, 20 to 25 minutes; drain and set aside. Wipe saucepan clean.

Step 4

Heat remaining 1 tablespoon oil in now-empty saucepan over medium heat until shimmering. Add fennel and shallot and cook until softened and lightly browned, 5 to 7 minutes. Stir in garlic, coriander, and thyme and cook until fragrant, about 30 seconds. Off heat, stir in cooked barley, ½ cup Parmesan, parsley, pine nuts, and butter. Season with salt and pepper to taste.

Step 5

Flip roasted squash over and scoop out flesh, leaving ⅛-inch thickness of flesh in each shell. Gently fold cooked squash into barley mixture, then mound mixture evenly in squash shells. Sprinkle with remaining ¼ cup Parmesan and bake on upper rack until heated through and cheese is melted, 5 to 10 minutes. Drizzle with vinegar to taste and serve.