Preheat the oven to 400°. Line a baking sheet with parchment paper.
Cut the squash in half, vertically and scoop out the seeds. Drizzle the cut side with olive oil and rub it into the flesh. Sprinkle with salt and place the squash cut-side-down onto the baking sheet. Roast for 20 minutes.
Meanwhile in a medium skillet, heat the olive oil over medium heat and add the onions and garlic. Saute for 2-3 minutes then stir in the chopped mushrooms, thyme, sage and salt, cook until the mushrooms release their liquid, about 5 minutes. Stir in the chopped kale and vegetable broth, cover and reduce heat to a simmer for 3-4 minutes until kale softens. Stir in the pepper, nutmeg and the cooked grains. Add the parmigiano reggiano and stir until just combined.
Tear the bread into large pieces and transfer to a mini prep food processor. Add the butter and pulse several times until it forms bread crumbs.
When the squash is done, fill the cavities with the stuffing and sprinkle with breadcrumbs and bake for an additional 10 minutes. If the breadcrumbs need additional browning, turn on the broiler and cook just until the breadcrumbs start to brown, (about a minute or two).
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Notes
You can also serve the squash with a little extra parmesan if you like.