Place potatoes in a pot of salted water, enough to cover. Bring to a boil and reduce heat, simmering about 10-15 minutes, until potatoes are tender. Drain.
Mix egg yolk in with milk. Mash or whip potatoes with butter and egg/milk mixture. Season generously with salt and pepper. Set aside.
!For Meat Filling:
Preheat oven to 400.
Put a large frying pan over medium heat. Add oil and, when hot, add onions and carrots. Cook 3 minutes. Toss in garlic. Cook another minute. Add meat and brown. Season generously with salt and pepper.
When meat is brown, sprinkle the meat with flour and stir. Add the tomato paste, worcestershire sauce, ketchup, and beef broth. Add herbs and veggies. Remove from heat.
In a 9inch deep-dish pie plate or oblong casserole, pour the meat mixture into dish. Spread the potatoes over top of the meat mixture. Sprinkle with cheddar cheese.
Bake 25 minutes or until potatoes and cheese begin to brown. Serve.