Adjust an oven rack to the middle position and heat the oven to 450°F. Line a rimmed baking sheet with parchment paper.

Toss the butternut squash with oil, salt, and pepper in a large bowl. Spread the pieces in a single layer on the prepared baking sheet and roast until the squash is tender and the edges are deeply golden brown, about 30 minutes.

Heat oil in a large Dutch oven or heavy-bottomed pot over medium heat. Add the onion and cook until softened and translucent, about 5 minutes.

Stir in the garlic and cook until fragrant, about 30 seconds. Add the barley and stir frequently to coat the grains in oil, cooking until they smell slightly toasted, about 2 minutes.

Pour in the vegetable broth and bring to a simmer. Reduce the heat to medium-low, cover, and cook until the barley is tender but still has a pleasant chew, and the liquid has thickened to a creamy consistency, 35 to 40 minutes. Stir occasionally toward the end of the cooking time to prevent the grains from sticking to the bottom of the pot.

Gently fold the roasted squash, sage, and nutmeg into the cooked barley. Taste and adjust with extra salt or pepper if needed, then serve immediately while the texture is velvety.