Step 1: Preheat oven to 400°F (200°C).
Step 2: In a large bowl, toss potatoes, bell pepper, and onion with 2 tbsp olive oil, salt, and pepper.
Step 3: Spread vegetables on a large rimmed baking sheet in a single layer.
Step 4: In the same bowl, combine balsamic vinegar, honey, garlic, thyme, and remaining 1 tbsp olive oil.
Step 5: Place chicken breasts on the baking sheet among the vegetables.
Step 6: Pour half of the balsamic mixture over the chicken, reserving the rest.
Step 7: Roast for 20 minutes.
Step 8: Remove pan from oven and pour reserved balsamic mixture and chicken broth over chicken and vegetables.
Step 9: Return to oven and roast for 10-15 more minutes until chicken reaches 165°F internal temperature.
Step 10: Garnish with fresh parsley if desired and serve immediately.