Preheat oven to 400°F (200°C).
Place cubed sweet potatoes in a large pot of salted water and bring to a boil. Cook for 15 minutes or until fork-tender.
Drain potatoes and mash with 1 tablespoon of olive oil and milk until smooth. Season with salt and pepper.
While potatoes boil, heat the remaining 1 tablespoon of olive oil in a large skillet over medium heat.
Add the diced onion and garlic, sautéing for 3-5 minutes until translucent.
Add ground turkey to the skillet and cook until browned, breaking it apart with a spoon.
Stir in the tomato paste, dried thyme, and dried rosemary.
Add the peas, carrots, and chicken broth. Simmer for 10 minutes until the sauce has thickened slightly.
Transfer the meat and vegetable mixture into a 2-quart baking dish.
Spread the mashed sweet potatoes evenly over the meat mixture. Use a fork to create textured ridges on the surface.
Bake for 20 minutes or until the edges are bubbling and the sweet potato topping is slightly golden.
Let stand for 5 minutes before serving.