01 - Preheat your oven to 400°F.
02 - Peel and cube the russet potatoes. Boil them in salted water until fork-tender, approximately 15 minutes. Drain thoroughly. In the same pot, mash the cooked potatoes with unsalted butter, warmed milk, salt, and pepper until a smooth consistency is achieved. Set aside.
03 - In a large skillet over medium heat, warm the olive oil. Add the finely chopped onion and sauté until softened, about 3 to 4 minutes. Incorporate the minced garlic and cook for an additional minute until fragrant.
04 - Add the ground beef to the skillet, breaking it apart with a spoon. Cook until it is thoroughly browned. If necessary, drain any excess fat.
05 - Stir in the tomato paste and all-purpose flour, cooking for 1 minute to toast the flour. Gradually whisk in the beef broth, Worcestershire sauce, dried thyme, and dried rosemary, ensuring no lumps.
06 - Bring the mixture to a simmer and cook for 5 minutes, allowing it to slightly thicken. Fold in the frozen peas and carrots. Season the beef filling generously with salt and black pepper to taste. Remove the skillet from the heat.
07 - Transfer the prepared beef mixture evenly into a 9x13-inch baking dish. Carefully spoon the mashed potato topping over the beef, spreading it smoothly with a spatula. For an appealing finish, create decorative ridges on the potato surface with a fork, if desired.
08 - Place the baking dish in the preheated oven and bake for 20 minutes, or until the mashed potato topping is golden brown and the filling is bubbling around the edges.
09 - Allow the shepherd's pie to rest for 5 minutes before portioning and serving.