Preheat oven to 400°F (200°C).
Scrub sweet potatoes and pierce multiple times with a fork. Place on a baking sheet and roast for 45 to 50 minutes until tender.
While potatoes roast, heat olive oil in a large skillet over medium heat. Add diced onion and sauté for 5 minutes until translucent.
Add minced garlic, frozen peas, and carrots. Cook for an additional 3 minutes.
In a small bowl, whisk cornstarch into the cold chicken bone broth until no lumps remain.
Pour the broth mixture into the skillet and bring to a simmer, stirring constantly until the sauce thickens.
Reduce heat to low. Fold in the shredded chicken, thyme, rosemary, salt, and pepper.
Remove skillet from heat and stir in the Greek yogurt until well incorporated and creamy.
Slice the roasted sweet potatoes lengthwise and fluff the interior with a fork. Divide the chicken pot pie filling equally among the four potatoes and serve immediately.