Begin by preparing the mashed potato topping; boil the potatoes until tender, then mash with milk and butter, season with salt and pepper, and set aside.
Sprinkle flour over the turkey mixture, stir, and cook for a minute. Pour in chicken broth and bring to a simmer. Add frozen vegetables, cook until mixture thickens, then transfer to a baking dish.
Spread the mashed potatoes over the turkey mixture in an even layer. Sprinkle with cheddar cheese and bake for 20-25 minutes until the top is golden and the edges are bubbly.