01 - Preheat the oven to 375°F (190°C).
02 - Heat olive oil and butter in a large, oven-safe skillet or Dutch oven over medium heat. Add the finely chopped onion and cook, stirring occasionally, until softened, around 5 minutes.
03 - Add the minced garlic and cook for an additional minute. Then add the sliced mushrooms and thyme leaves. Sauté until mushrooms are golden and have released their juices, about 8 minutes.
04 - Stir in the rinsed pearl barley and coat it well for 2 minutes. Pour in the white wine and cook until nearly evaporated, approximately 2 minutes.
05 - Add the warmed vegetable broth and bring to a gentle simmer. Season with salt and freshly ground black pepper according to taste.
06 - Cover the skillet or Dutch oven tightly with its lid or foil and transfer to the preheated oven. Bake for 35 to 40 minutes, stirring halfway through, until the barley is tender and most of the liquid has been absorbed.
07 - Remove from the oven and stir in the grated Parmesan cheese, frozen peas if using, and chopped parsley. Adjust seasoning if necessary.
08 - Serve hot, garnished with additional Parmesan cheese and parsley as desired.