Broiled Lemon Chicken with Carrot-Parsley Sauce

Ingredients

• 4 skinless, boneless chicken breast halves (1 lb total)
• 1 1/2 tsp grated lemon zest
• 1 tbsp plus 2 tsp fresh lemon juice
• 2 garlic cloves, crushed through a press
• 1/2 tsp thyme
• 1/4 tsp salt
• 1/4 tsp black pepper
• 1 cup carrot juice
• 1 tbsp cornstarch
• large pinch cayenne pepper
• 2 tbsp chopped parsley, preferably flat leaf