Mushroom Barley and Roasted Asparagus Salad

Name: Mushroom Barley and Roasted Asparagus Salad
Ingredients: 3/4 cup pearl barley, rinsed; 2 sprigs fresh thyme, plus 1 tablespoon minced leaves; 3 stems fresh flat-leaf parsley, plus 1/3 cup chopped leaves; 1 bay leaf; 2 lemons, zest peeled in large strips; 10 ounces button mushrooms, trimmed and thinly sliced (about 4 cups); 1/3 cup freshly squeezed lemon juice; 2 teaspoons kosher salt; 2 teaspoons Dijon mustard; Freshly ground black pepper; 1/3 cup extra-virgin olive oil, plus more for cooking the asparagus; 1/2 medium shallot, minced; 2 bunches medium asparagus, woody stems trimmed (about 2 pounds)