01 - Set oven temperature to 400°F.
02 - Boil a large pot of salted water; add potatoes and cook until tender, approximately 15 minutes. Drain thoroughly.
03 - Mash potatoes with milk and butter. Season with salt and pepper. Optionally, fold in grated cheddar cheese for richness.
04 - Heat olive oil in a skillet over medium heat; cook onion and garlic until softened, about 3 minutes.
05 - Add diced carrots; cook for 4 to 5 minutes while stirring frequently.
06 - Incorporate ground beef; break apart and cook until no pink remains, 6 to 8 minutes. Drain excess fat if necessary.
07 - Stir in tomato paste, Worcestershire sauce, thyme, rosemary, salt, and pepper; cook for 2 minutes.
08 - Sprinkle flour over filling; stir to coat. Pour in beef broth and bring to a simmer.
09 - Mix in peas; simmer 3 to 4 minutes until slightly thickened. Adjust seasoning as needed.
10 - Transfer filling to a 2-quart baking dish.
11 - Evenly spread mashed potato mixture over filling; create decorative ridges with a fork.
12 - Bake for 25 to 30 minutes until the topping is golden and filling is bubbling.
13 - Allow to rest for 10 minutes before serving.