Preheat the oven to 400°F. Heat a large skillet over medium heat and add the ground turkey. Cook until no longer pink, breaking it up as it browns.
Add the diced onion and carrots to the skillet. Cook for 5 minutes until the vegetables start to soften. Stir in the minced garlic and cook 1 minute more.
Sprinkle the flour over the turkey mixture and stir for 1 minute. Slowly pour in the chicken broth and Worcestershire sauce. Add the peas, salt, pepper, and thyme. Simmer for 3 to 4 minutes until the sauce thickens slightly.
While the filling simmers, place the cubed potatoes and whole garlic cloves in a medium saucepan. Cover with water and bring to a boil. Cook until the potatoes are tender, about 12 minutes.
Drain the potatoes and return them to the saucepan. Add the butter, milk, salt, and pepper. Mash until smooth and creamy.
Spread the turkey filling evenly in a 9x9 baking dish. Spoon the garlic mashed potatoes over the top and spread to cover completely.
Bake for 20 minutes until the potato topping is lightly golden at the edges. Let rest 5 minutes before serving.