Pour vegetable or chicken broth into a saucepan and heat over low heat, keeping it at a gentle simmer.
In a large, heavy-bottomed pot, heat olive oil over medium heat. Add onion and garlic, cooking until translucent and aromatic, about 3 to 4 minutes.
Stir in the pearl barley and cook for 2 to 3 minutes, stirring regularly, until the edges look slightly translucent.
Pour in the white wine, scraping up any browned bits on the bottom, and stir gently until the wine is almost completely absorbed.
Pour a ladleful of warm broth into the barley, stirring constantly until liquid is almost gone. Repeat, adding broth one ladle at a time for 25 minutes.
Fold the sautéed mushrooms and thyme into the creamy barley when it’s just tender, stirring gently until everything is heated through, about 2 minutes.
Remove from heat, stir in grated Parmesan cheese, season with salt and pepper to taste. Let rest for 2 minutes to thicken slightly before serving.