Preheat the oven to 400°F. Place the sweet potato cubes in a pot, cover with water, and bring to a boil. Cook for 12-15 minutes until tender, then drain.
While the sweet potatoes cook, heat a large skillet over medium heat. Add the ground turkey and cook, breaking it up with a spoon, until no longer pink, about 6-7 minutes.
Add the onion, carrots, and garlic to the skillet. Cook for 4-5 minutes until the vegetables begin to soften.
Stir in the tomato paste, thyme, salt, and pepper. Pour in the chicken broth and add the frozen peas. Simmer for 5 minutes until the mixture thickens slightly.
Mash the drained sweet potatoes with the butter and milk until smooth. Spread the turkey filling evenly in a baking dish, then spoon the sweet potato mash over the top.
Sprinkle the shredded cheddar cheese over the mash. Bake for 15-20 minutes until the topping is lightly golden and the filling is bubbling at the edges.