Cook the potatoes: Boil potatoes in salted water until soft (about 15 minutes). Drain, mash with butter and milk. Add salt. Set aside.
Prepare the meat filling: In a pan, heat olive oil. Sauté onion, carrot, and garlic until soft. Add ground beef and cook until browned.
Add seasonings: Stir in tomato paste, Worcestershire sauce, and beef broth. Simmer for 10 minutes. Mix in peas. Season with salt and pepper.
Assemble the pie: Spread meat filling in a baking dish. Top evenly with mashed potatoes. Use a fork to create texture.
Bake: Bake in a preheated oven at 200°C (400°F) for 20–25 minutes, or until the top is golden.