Preheat oven: Preheat your oven to 375°F (190°C).

Cook filling: In a large skillet, brown the ground meat over medium heat. Drain any excess fat. Add the onion, carrot, celery, garlic, Worcestershire sauce, thyme, salt, and pepper. Cook until vegetables are softened, about 5 minutes. Stir in the diced tomatoes, corn, and green beans. Bring to a simmer and cook for 10-15 minutes, or until heated through.

Make mashed potatoes: Cook the potatoes in boiling salted water until tender. Drain and mash with the milk, butter, salt, and pepper.

Assemble shepherd's pie: Pour the meat and vegetable mixture into a 9x13 inch baking dish. Top with the mashed potatoes.

Bake: Bake for 30-35 minutes, or until the mashed potatoes are golden brown and the filling is bubbly.

Serve: Serve hot, accompanied by your favorite side dishes.

Tips:

For a spicier shepherd's pie, add a pinch of cayenne pepper or a dash of hot sauce to the filling.

You can use other vegetables in your shepherd's pie, such as peas, mushrooms, or spinach.

For a vegetarian shepherd's pie, substitute the ground meat with lentils or vegetable protein.

Serve with a side salad or a crusty bread.

Enjoy your classic shepherd's pie!