In a cast iron skillet sautee onion, carrot, and meat. Cook until browned, 8 to 10 minutes.
Drain the fat and add the broth, tomato paste, and herbs. Simmer until the juices thicken, about 10 minutes, then add the peas.
Meanwhile, bring the potatoes to a boil in salted water. Cook until tender, about 20 minutes; drain. Mash the potatoes with the butter, milk, and salt.
Spread the potatoes over the meat mixture. Top with cheddar cheese.