Creamy Spring Barley

Name: Creamy Spring Barley
Ingredients: 1 bunch asparagus, thinly sliced into 1/4-inch rounds; 1/2 cup peas; 3 tablespoons unsalted butter, divided; 2 tablespoons extra-virgin olive oil, divided; 2 cups barley, rinsed; 6 cups chicken stock; 2 tablespoons parsley, chopped; 1/4 cup grated Parmesan cheese, plus more for serving; Salt and freshly cracked pepper; Lemon zest, to taste; Chives, for garnish