Preheat the oven to 400°F and line a baking sheet with parchment paper. Brush the cut sides of the acorn squash with a portion of the olive oil and season generously with salt and pepper.

Place the squash halves cut-side down on the prepared baking sheet. Roast until the flesh is very tender and the skin is easily pierced with a fork, about 40 to 45 minutes.

Bring a medium pot of salted water to a boil while the squash roasts. Add the barley, reduce the heat to medium-low, and simmer until the grains are tender but still have a pleasant chew, about 25 to 30 minutes. Drain the barley thoroughly.

Heat the remaining olive oil in a large skillet over medium heat until it shimmers. Add the onion and fennel and cook, stirring occasionally, until the vegetables are softened and just beginning to brown around the edges, about 8 to 10 minutes.

Add the garlic, thyme, and coriander to the skillet. Cook until the garlic is fragrant and the spices smell toasted, about 30 seconds. Remove the skillet from the heat.

Fold the cooked barley, half of the Parmesan, the parsley, toasted pine nuts, and butter into the onion mixture. Stir until the butter is melted and the filling is well combined, then season with salt and pepper to taste.

Turn the roasted squash halves cut-side up. Divide the barley filling evenly among the cavities, mounding it slightly in the center. Sprinkle the remaining Parmesan over the tops.

Return the stuffed squash to the oven and bake until the filling is heated through and the cheese has melted into a light golden crust, about 5 to 8 minutes.

Transfer the squash to individual plates and drizzle each half with balsamic vinegar. Serve hot while the cheese is still melty.