Cook the potatoes. Place the potatoes in a pot on the stove and cover with cold water. Turn the heat to high and bring to a boil. Cook for 13-15 minutes, or until the potatoes are soft when pierced with a fork.
Mash the potatoes. Drain the potatoes in a colander, then return to the pot. Add the cheese, milk, butter, salt and pepper and mash until creamy.
Saute the onion and garlic. Preheat your oven to 400 degrees fahrenheit (200 celsius). In a large oven-safe saute pan, heat the oil on medium heat. Add the onion and garlic and saute for a minute.
Add more veggies and meat. Add the diced carrots, diced celery, and beef. Cook for 8 to 10 minutes or until the meat is browned. Use your spatula to break up the meat while cooking.
Add the flavor. Drain any fat from the pan and add the broth, tomato paste, Worcestershire sauce, rosemary, thyme, salt and pepper. Simmer for about 5 minutes, until the sauce is slightly thickened.
Add the peas. Add the frozen peas and stir together. Turn off the stove and use the back of your spatula to flatten the meat mixture into a single layer in the pan.
Top with mashed potatoes. Dollop the cheesy mashed potatoes on top of the meat and use a spoon or spatula to spread it flat to the edges. If desired, create texture in the potato topping with a spoon or fork.
Bake. Bake the cottage pie until slightly golden, about 25 to 30 minutes. You can broil the top for 1 to 2 minutes as well.