Spring Vegetable Penne with Lemon Cream Sauce {Gluten-free}

The original recipe from Cooking Light, can be found here. I made some alterations, such as adding chicken and omitting gluten

• 1 tablespoon extra-virgin olive oil
• 2 boneless skinless chicken breasts, cut into small pieces
• 
  • 1 tablespoon extra-virgin olive oil 
  • 3/4 cup chopped Vidalia or other sweet onion
  • 1 (4-ounce) package presliced mushrooms 
  • 1 teaspoon chopped fresh thyme
  • 1 garlic clove, minced 
  • 1 tablespoon all-purpose flour
  • 1/2 cup fat-free, lower-sodium chicken broth
  • 1/2 cup half-and-half
  • 3/4 cup frozen green peas
  • 3 tablespoons shaved Parmesan cheese, divided
  • 1/2 teaspoon grated lemon rind 
  • 1 tablespoon fresh lemon juice 
  • 1/2 teaspoon salt
  • 1/2 teaspoon freshly ground black pepper
  • 8 ounces uncooked penne 
  • 1 pound (1-inch) diagonally cut asparagus

• 1 pound (1-inch) diagonally cut asparagus (I used broccoli because asparagus was 4.99/lb