Preheat the oven to 425 degrees F.
Toss the carrot, celery root, and butternut squash with 2 tablespoons of the olive oil and the salt on a baking sheet and spread out in an even layer. Roast until golden and tender, about 25 minutes.
Combine the chicken broth and thyme in a small saucepan and bring to a simmer.
Heat the remaining 2 tablespoons olive oil in the saucepan over medium-high heat. Add the barley, onion and garlic, and cook, stirring occasionally, until the vegetables soften a bit, about 5 minutes. Pour in the wine, and cook, stirring constantly, until the liquid is absorbed. Add 2 cups of the broth, reduce the heat to medium-low, and simmer until the liquid is absorbed, stirring frequently. Add the remaining broth and simmer, stirring occasionally, until the barley is tender but still slightly firm and the mixture is still soupy, about 30 minutes. Add the roasted vegetables and cook until the vegetables are heated through. Stir the mustard greens into the risotto, then let the mixture sit until the greens wilt, about 3 minutes. If the risotto thickens up too much, thin it out with a little hot water. Season with salt and pepper. Serve immediately. Pass grated cheese at the table.
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