COOK IT.
Preheat your grill or smoker to 350-375°F (175-190°C)
While the grill preheats, prep the pie filling on the stove. In a large skillet over medium heat, cook the ground beef or lamb, onions, and garlic until the meat is well browned and the onions are tender. Drain off any excess fat.
Stir in the vegetables, beef broth, tomato paste, Worcestershire sauce, and salt and pepper. Let it simmer while you prepare the mashed potatoes.
In a large pot of water, boil the peeled and chopped potatoes until tender. Drain and return them to the pot. Add the milk and butter, then mash until smooth. Season with salt and pepper.
Using a grill-safe baking dish (like a roaster pan or cast iron), add the meat and veggie mixture to the bottom. Then, top with the mashed potatoes, making sure they are spread to the edges. Sprinkle shredded cheese all over the top.
Place in the preheated grill where there is indirect heat. Close the lid and bake for 25-30 minutes, or until the pie is hot and the cheese is melted and browned.
Remove from the grill and allow to cool for 5 minutes before serving.