Heat oven to 400°F with racks in the upper-middle and lower-middle positions. Line a rimmed baking sheet with aluminum foil and grease with oil. Brush the cut sides of the squash with oil, season generously with salt and pepper, and place them cut-side down on the prepared sheet. Roast on the lower-middle rack until the flesh is tender and a paring knife offers no resistance, 45 to 55 minutes. Increase the oven temperature to 450°F after removing the squash.

Bring water to a boil in a large saucepan and stir in the barley and a pinch of salt. Reduce heat to a simmer and cook until the grains are tender but still have a slight chew, 20 to 25 minutes. Drain thoroughly.

Wipe the saucepan dry and heat the remaining oil over medium heat until it shimmers. Sauté the onion and fennel until they are softened and translucent, about 10 minutes. Stir in the garlic, thyme, and coriander and cook until the aromatics are fragrant.

Remove the pan from the heat and stir in the cooked barley, three-quarters of the Parmesan, parsley, pine nuts, and butter. Season with salt and pepper, tasting to ensure the flavors are balanced.

Flip the roasted squash halves over. Carefully scoop out the flesh into a bowl, leaving a 1/8-inch thickness of flesh in each shell to provide a sturdy base. Gently fold the scooped flesh into the barley mixture, then mound the filling into the squash shells.

Sprinkle the remaining Parmesan over the tops and bake on the upper-middle rack until the cheese is melted and lightly browned, 5 to 10 minutes. Drizzle with balsamic vinegar and serve hot.