Melt the butter in a large pot over medium heat. Add the onion, ½ teaspoon salt, and ¼ teaspoon pepper and cook, stirring occasionally, until tender, 6 to 8 minutes. Add the wine and cook until syrupy, 5 to 7 minutes.
Add the broth and barley and bring to a boil. Reduce heat and simmer, stirring occasionally, until almost tender, 24 to 26 minutes. Add the squash and cook, stirring occasionally, until the barley and squash are tender, 25 to 35 minutes more (adding more liquid if the risotto becomes too thick before the barley and squash are tender). Stir in the Parmesan.
Serve topped with additional shaved Parmesan.