Preheat your oven to 375°F (190°C).
In a large skillet over medium-high heat, cook the ground venison, breaking it up with a wooden spoon, until browned, about 5-7 minutes.
Sauté the onion, carrots, celery, and garlic in the skillet. Cook the vegetables for about 5 minutes until softened. .
Stir in the tomato paste, Worcestershire sauce, and flour. Cook for 1 minute, then gradually pour in the broth, stirring constantly to prevent lumps.
Cook the mixture on a gentle simmer until it reaches a thick consistency, about 5 minutes . Season with thyme, salt, and pepper.
While waiting, add the diced potatoes to a large pot and submerge them in cold water. Heat the pot to bring the water to a boil, then cook the potatoes for approximately 15 minutes, or until they become tender.
Mash the potatoes with milk and butter until they’re smooth and creamy.
Transfer the venison mixture to a 9x13-inch baking dish. Top with the mashed potatoes and sprinkle with the cheddar cheese.
Bake the dish for 30-35 minutes, until the top forms a golden-brown crust and the filling bubbles beautifully.
Allow the shepherd’s pie to rest for 5 minutes before serving for the best flavor and texture