Preheat oven to 375°F (190°C). Lightly grease a baking dish.
Boil sweet potatoes in salted water until fork-tender, about 12–15 minutes. Drain and mash with Greek yogurt, butter (if using), salt, and pepper. Set aside.
Heat olive oil in a large skillet over medium heat. Add ground turkey and cook until browned.
Add onion, garlic, and carrots. Cook for 4–5 minutes until softened.
Stir in tomato paste, thyme, smoked paprika, salt, and pepper.
Pour in chicken broth and simmer for 5–7 minutes until slightly thickened.
Stir in peas, then transfer mixture to prepared baking dish.
Spread mashed sweet potatoes evenly over the top.
Bake uncovered for 25–30 minutes until heated through and lightly golden on top.