Boil the sweet potatoes. Add the peeled, cubed sweet potatoes to a pot of salted water and boil until fork-tender, about 15 minutes. Drain, then mash with the milk and butter and season with salt and pepper.
Cook the filling. Heat the olive oil in a large skillet over medium-high heat. Add the ground turkey, onion, and carrots and cook, breaking up the turkey, until browned and the vegetables soften, about 8 minutes.
Season. Stir in the peas, chicken broth, tomato paste, thyme, salt, and pepper. Simmer for about 5 minutes, until slightly thickened.
Assemble. Transfer the filling to a baking dish. Spread the mashed sweet potatoes evenly over the top and sprinkle with the cheddar.
Bake. Bake at 375 degrees F for 25 to 30 minutes, until hot and bubbly and the cheese is melted. Let rest a few minutes before serving.