Prepare the mashed potatoes: Place the chopped potatoes in a large pot and cover with cold water. Bring to a boil and cook for 12-15 minutes or until tender when pierced with a fork. Drain and return the potatoes to the pot. Add butter, milk, salt, and pepper, and mash until smooth and creamy. Set aside.

1. Cook the filling: In a large skillet, heat the olive oil over medium heat. Add the chopped onion and cook for 2-3 minutes until softened. Add the minced garlic and cook for another 30 seconds until fragrant.
2. Brown the meat: Add the ground beef (or lamb) to the skillet and cook, breaking it apart with a spoon, until browned and fully cooked, about 5-7 minutes. Drain any excess fat.
3. Make the gravy: Stir in the tomato paste and Worcestershire sauce. Sprinkle the gluten-free flour (or cornstarch) over the meat mixture and stir to combine. Gradually pour in the beef broth, stirring constantly to prevent lumps. Add the thyme, rosemary, salt, and pepper. Simmer for 5-7 minutes until the gravy thickens and the vegetables are tender. Stir in the frozen peas and cook for an additional 2 minutes. Remove from heat.
4. Assemble the cottage pie: Preheat your oven to 400°F (200°C). Transfer the meat and vegetable filling into a greased 9×9-inch baking dish or similar-sized oven-safe dish. Spoon the mashed potatoes on top of the filling, spreading them evenly with a spatula. Use the back of a spoon to create a textured surface on top of the potatoes.
5. Bake: Place the casserole dish in the oven and bake for 20-25 minutes, or until the top is golden brown and the filling is bubbling around the edges.
6. Serve: Let the cottage pie rest for a few minutes before serving. Serve hot with a side salad or steamed vegetables for a complete meal.