Preheat the oven to 450 degrees F.
Slice the squash in half lengthwise and scoop out the seeds. Drizzle a large baking dish with 1 tablespoon of olive oil. Place the squash halves cut-side down in a large baking dish. Pierce the skin of the squash a few times with a knife.
Bake the squash until it is tender when pierced with a fork, 30-40 minutes, depending on size.
While the squash cooks, cook the quinoa by bringing the stock to boil in a small saucepan. Add the quinoa and stir once. Reduce the heat to low-medium and cover with a lid. Cook, covered for 15 minutes. Remove the pan from the heat.
Heat a large skillet over medium heat. Add 1 tablespoon of olive oil. When the oil begins to shimmer, add the shallots, garlic, pecans, and dried thyme. Cook, stirring often, until the shallots are very tender and the pecans are fragrant, about 5 minutes. Transfer the shallots and pecans to a large mixing bowl.
When the squash is done roasting, remove it from the oven and let it cool until you can safely hold it on a cutting board (using a clean dish towel to hold it in place helps).
Use a spoon or an ice cream scoop to scrape the flesh out of the roasted squash halves, leaving a layer of about 1/2 inch of squash remaining in the shell.
As you scoop out the squash, add it to the bowl with the shallots and pecans. Add the salt and vinegar. Mash everything together until even.
Add the quinoa to the mashed squash and gently fold it in.
Return the squash halves to the baking dish, cut-side up. Spoon the filling into the prepared squash halves.
Stir together the melted butter, panko breadcrumbs, and cheese. Press the panko crust into the tops of the squash.
Return squash to the oven and bake, uncovered, until the crust is golden brown, 15 to 20 minutes.
Sprinkle with parsley. Serve warm.