Preheat an oven to 400°F (200°C). Line an 18” x 13” half sheet pan with parchment paper.

In a bowl, toss the squash with 2 Tbs. of the olive oil. Spread in a single layer on the prepared baking sheet and season well with salt and pepper. Roast, stirring once, until tender and caramelized, 30 to 35 minutes. Set aside.

In a small saucepan over low heat, warm 4 cups of broth.

In a large saucepan over medium heat, warm the remaining 2 Tbs. olive oil. Add the garlic and shallots and cook until softened, about 5 minutes. Add the sage and thyme, and season with salt and pepper. Stir to combine and cook until fragrant, about 1 minute. Add the barley and cook, stirring often, until toasted, about 2 minutes. Add the wine and cook, stirring occasionally, until it is evaporated.

Reduce the heat to medium-low. While continuously stirring, slowly add 1 cup (8 fl. oz./250 ml) of the broth until the liquid is completely absorbed, about 5 minutes. Repeat this process 1 cup at a time with the remaining broth. Allow each addition to be absorbed before adding more.

When the barley is tender and the risotto is creamy, remove from the heat. Stir in the squash and cheese. Season with salt and pepper and serve immediately.