In a large saucepan, heat 3 tbsp. oil over medium. Add the shallots and garlic and cook, stirring occasionally, until softened, about 3 minutes. Stir in the barley and sage; add the stock and bring to a boil. Cover; reduce heat to low. Cook, stirring occasionally, until the barley is tender, about 40 minutes. Uncover and cook until the liquid is almost absorbed and the sauce is creamy, 3 to 5 minutes.
Meanwhile, in a large skillet, heat the remaining 2 tbsp. oil over medium-high. Add the Brussels sprouts, season with salt and pepper and cook, stirring occasionally, until browned and tender, 6 to 8 minutes.
Stir the vinegar, half the Brussels sprouts and half the cheese into the risotto; season. Divide among plates. Drizzle with oil and top with the remaining Brussels sprouts and cheese.
