Heat a large oven-safe skillet over medium heat and add the ground turkey. Cook until browned, breaking it up with a spoon as it cooks.
Add the diced onion and carrots to the skillet. Cook for 5 minutes until the vegetables begin to soften.
Stir in the minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the mixture and stir to coat everything evenly. Cook for 1 minute.
Pour in the chicken broth and add the rosemary, salt, and pepper. Stir well and simmer for 3 minutes until the mixture thickens slightly.
Stir in the frozen peas and remove the skillet from the heat.
Spread the mashed potatoes evenly over the turkey mixture in the skillet. Use a spoon or spatula to create a smooth layer.
Brush the top of the potatoes with melted butter and sprinkle with paprika.
Place the skillet under the broiler for 3 to 5 minutes until the potato crust turns lightly golden.