How to Make It
Whisk balsamic, 1 tablespoon oil, and ¼ teaspoon salt in a large bowl; set aside.
Bring broth and 3½ cups water to a simmer in a saucepan over medium. Keep at a low simmer.
Heat remaining 2 tablespoons oil in a large skillet over medium-high. Add barley, onion, garlic, and remaining ½ teaspoon salt. Cook, stirring often, until barley is toasted and onion softens, about 6 minutes. Add wine and cook, stirring often, for 30 seconds. Ladle 1 cup broth mixture into skillet and cook, stirring constantly, until liquid is absorbed, about 1 minute. Ladle in remaining broth mixture, ½ to ¾ cup at a time, stirring often, until liquid is absorbed between additions, 25 to 30 minutes. Stir in grated cheese. Add up to ½ cup water to loosen consistency, if needed.
Toss radicchio, parsley, and hazelnuts with balsamic mixture. Serve with risotto. Top with shaved cheese.