Preheat the Oven: Preheat your oven to 400°F (200°C).
Prepare the Meat Filling: In a large skillet, heat the olive oil over medium heat. Add the chopped onion and minced garlic, sautéing until translucent. Add the ground beef or lamb, cooking until browned. Drain any excess fat.
Add Vegetables and Seasoning: Stir in the tomato paste, Worcestershire sauce, dried thyme, dried rosemary, salt, and pepper. Add the frozen peas and carrots, mixing well. Pour in the beef broth and let the mixture simmer for about 5 minutes until slightly thickened.
Prepare the Mashed Potatoes: In a mixing bowl, combine the prepared mashed potatoes with milk and butter, mixing until smooth and creamy. Season with salt and pepper to taste.
Assemble the Shepherd's Pie: Spread the meat and vegetable mixture evenly in the bottom of the baking dish. Top with an even layer of mashed potatoes, spreading them out to cover the filling completely. For an extra touch, sprinkle shredded cheddar cheese on top.
Bake: Place the baking dish in the preheated oven and bake for 20-25 minutes, or until the top is golden brown and the filling is bubbling around the edges.
Rest and Serve: Let the baked shepherd's pie rest for 10 minutes before serving.