In a large saucepan, combine 1 cup of the broth, 1 cup of water, the onion, and garlic. Bring to a boil and stir in the barley. Reduce to a simmer, cover, and cook until the barley is tender, about 30 minutes.
Meanwhile, in a nonstick Dutch oven or large pot, heat oil until hot but not smoking over medium heat. Add the rutabaga and carrots and cook, stirring frequently, until the rutabaga is golden brown, about 5 minutes. Add the turnips and parsnips and cook, stirring frequently, until the turnips and parsnips are lightly brown, about 5 minutes.
Add the apples, stirring to coat. Stir in the rosemary, salt and pepper. Add the remaining 2 1/2 cups broth and bring to a boil. Reduce to a simmer, cover, and cook until the vegetables and apples are tender, about 15 minutes longer. Stir in the barley mixture and lemon juice. Divide among 4 bowls and serve.