How to Make It
Fill a large bowl with ice water. Cook peas in a pot of boiling salted water until crisp-tender, about 2 minutes. Transfer to ice water to cool; drain.
Bring broth, 2½ cups water, Parmesan rind, and bay leaf to a simmer in a large pot. Keep warm over low heat.
Heat 2 tablespoons oil in a large saucepan over medium. Add onion and garlic and cook, stirring, until softened, about 4 minutes. Add barley and ¼ teaspoon salt and cook, stirring, until lightly toasted, about 5 minutes. Add wine and cook, stirring, until absorbed, about 30 seconds.
Stir 1 cup warm broth into barley and cook, stirring, until liquid is nearly absorbed, about 5 minutes. Continue cooking, adding ½ cup warm broth at a time, stirring until liquid is nearly absorbed after each addition, until barley is tender, about 40 minutes. (You should have ½ cup broth remaining.) Remove Parmesan rind and bay leaf. Stir in peas, pepper, 1 cup grated Parmesan, and remaining 1 teaspoon salt.
Cook, stirring, until peas are tender, about 2 minutes. Remove from heat and stir in remaining ½ cup broth. Top with pea shoots and remaining ½ cup Parmesan. Drizzle with remaining 2 tablespoons oil.