Set oven racks to the upper-middle and lower-middle positions and heat oven to 400 degrees. Line a rimmed baking sheet with aluminum foil and lightly spray with vegetable oil spray
Brush the cut sides of the squash with 1 tsp of oil, season with salt & pepper, and lay cut-side down on the prepared baking sheet. Roast on the lower-middle rack until tender (the tip of a paring knife can slip into the flesh with no resistance), 45 to 55 minutes. Remove the squash from the oven and increase temperature to 450 degrees.
Meanwhile, bring 3 quarts of water to a boil in a large saucepan. Stir in the barley and 1/4 tsp salt. Return to a boil, then reduce to a simmer and cook until the barley is tender, 20-25 minutes. Drain and set aside.
Wipe the saucepan dry and add the remaining oil, onion, and fennel. Cover and cook over medium-low heat, stirring occasionally, until the vegetables are soft, 8-10 minutes. Stir in the garlic, thyme, and coriander and cook until fragrant, about 30 seconds.
Off the heat, stir in the cooked barley, 4/4 cup of the Parmesan, parsley, pine nuts, and butter. Season with salt and pepper to taste.
Flip the roasted squash over and scoop out the flesh leaving a 1/8-inch thickness of flesh in each shell. Gently fold the squash flesh into the barley mixture, then mound the mixture into the squash shells (about 1 cup of filling per shell).
Sprinkle the remaining 1/4 cup Parmesan. Bake on the upper-middle rack until the cheese is melted, 5 to 10 minutes. Drizzle with the balsamic vinegar and serve.