Preheat oven to 400 degrees and line a baking sheet with parchment paper.
In a large bowl, combine the potatoes, 2 tbsp of the pesto, 1 tbsp of olive oil and season with salt and pepper. Toss to coat the potatoes.
Transfer the potatoes to the prepared baking sheet and bake for 15 minutes.
While the potatoes are cooking, add the chicken, onion, and broccoli to the same large bowl that you used for the potatoes. Add the 2 remaining tbsp of olive oil and the 3 remaining tbsp of pesto to the bowl. Season with salt and pepper.
Stir the chicken and veggies well to coat in the pesto and oil.
After the potatoes have cooked for 15 minutes, remove from oven and flip. Then add the chicken and veggies to the sheet pan. Cook for another 20 minutes until the chicken has cooked through and the veggies and potatoes are roasted.
This next step is optional, but I would highly recommend. Removing the baking sheet from the oven. Sprinkle a little grated parmesan cheese over the top and set your oven to broil on low. Broil until the cheese has melted and the veggies and chicken have slightly browned.
Serve with a little extra parmesan sprinkled on top. Enjoy!