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.
Drain the potatoes in a colander, then return to the pot. Add the milk, butter, salt and pepper and mash until creamy.
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. Then add the diced carrots, diced celery, and lamb. Cook for 8-10 minutes or until the meat is browned. Use your spatula to break up the meat while cooking.
Drain the 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 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.
Dollop the 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 the Shepherd's pie until slightly golden, about 25-30 minutes. You can broil the top for 1-2 minutes as well.