Heat 1 tablespoon of the butter and 1 tablespoon of the oil in a 12-inch saute pan over medium-high heat. When hot, add the shallot and cook, stirring until tender, 1 to 2 minutes. Add the barley, salt and pepper and cook for 1 minute. Pour in the wine and cook, stirring, until the wine is evaporated, 1 to 2 minutes. Transfer to the crock of a 6-quart slow cooker.

Add 2 tablespoons of the remaining butter and the remaining 1 tablespoon oil to the saute pan over medium-high heat. Add the mushrooms and cook until lightly browned and wilted and the fat has been absorbed, 4 to 5 minutes.

Add the mushrooms, squash, and stock to the slow cooker. Stir gently to combine. Set the slow cooker to low and cook until the liquid is absorbed and the barley and squash are tender, 2 1/2 to 3 hours, stirring occasionally to ensure that all the grains are evenly cooked. Remove the lid and stir in the parsley, sage, 1/2 cup of the Parmesan, and the remaining 2 tablespoons butter. Serve the risotto hot, garnished with the remaining cheese and additional pepper if desired.