Adjust the oven racks to the upper-middle and lower-middle positions and heat the oven to 400 degrees. Line a rimmed baking sheet with aluminum foil and grease it with a portion of the oil. Brush the cut sides of the squash with oil, season with salt and pepper, and lay them cut-side down on the prepared baking sheet. Roast on the lower-middle rack until a paring knife can be slipped into the flesh with no resistance, 45 to 55 minutes. Remove the squash from the oven and increase the oven temperature to 450 degrees.

Bring 3 quarts of water to a boil in a large saucepan. Stir in the barley and a pinch of salt. Return to a boil, then reduce the heat to a simmer and cook until the barley is tender, 20 to 25 minutes; drain thoroughly.

Wipe the now-empty saucepan dry, add the remaining tablespoon of oil, and heat over medium heat until shimmering. Add the onion and fennel and cook until softened and translucent, about 10 minutes. Stir in the garlic, thyme, and coriander and cook until fragrant.

Remove the pan from the heat and stir in the cooked barley, a large portion 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 an 1/8-inch thickness of flesh in each shell so they keep their shape. Gently fold the scooped-out squash flesh into the barley mixture. Spoon the mixture back into the squash shells, mounding it slightly, and sprinkle with the remaining Parmesan.

Bake the stuffed shells on the upper-middle rack until the cheese is lightly browned and bubbling, 5 to 10 minutes. Drizzle with balsamic vinegar and serve hot.