In a large, deep skillet, heat 2 Tbsp of the butter over medium heat. Add the onions and garlic and cook, stirring, until starting to soften. Add the mushrooms and thyme leaves and season with salt and pepper.
Cook, stirring regularly until mushrooms are tender and lightly golden, about 5-6 minutes. Add the drained tinned barley and the remaining 1 Tbsp butter. Cook, stirring, for about 1 minute.
Add 1 ladle of the stock and stir to combine. Cook over medium heat, stirring once or twice, until nearly most of the stock has been absorbed. The barley is cooked so it shouldn't take long. When cooked, stir in grated cheese and stir to combine.
Season dish with salt and freshly ground pepper, to taste. Serve with additional grated cheese and garnish with fresh thyme sprigs or fresh thyme leaves.