Heat the olive oil in a large skillet over medium-high heat. Add the onions and 1/8 teaspoon each salt and pepper and cook, stirring occasionally, until lightly browned, about 5 minutes. Add the mushrooms and cook, stirring occasionally, until browned, about 2 minutes. Stir in the barley and thyme and cook, stirring, until the barley is just golden, about 2 minutes.
Transfer to a 6-quart slow cooker and add the carrots, broth, 1 1/2 cups water and 1/4 teaspoon salt. Cover and cook on high until the liquid is absorbed and the carrots and barley are tender, about 3 hours.
Discard the thyme and stir in the Parmesan, vinegar, 1/2 teaspoon salt and 1/4 teaspoon pepper. Thin out the risotto with warm water for desired consistency as needed. Top with parsley and season to taste with salt and pepper.