Place the potatoes in a large pot and cover with cold water. Bring to a boil over medium high heat and cook for 13 to 15 minutes, or until the potatoes are fork tender.
Once fork tender, drain the potatoes, then return to the pot. Add the milk, butter, cheddar, salt and pepper and mash until creamy.
Preheat your oven to 400°F. In a large oven-safe baking dish, heat the oil over medium heat. Add the onion, diced carrots, diced celery, and saute for 5-10 minutes. Add the garlic the last minute and saute until fragrant. Add the beef and cook for another 8 to 10 minutes, breaking up as needed, until the meat is browned.
Add the stock, tomato paste, Worcestershire sauce, thyme, salt and pepper. Simmer for about 5 minutes, until the sauce is slightly thickened. Add the frozen peas and stir together. Remove from the heat and flatten the meat mixture into a single layer. Dollop the mashed potatoes on top of the meat and use a spoon to spread it flat to the edges, swooping the spoon to create some peaks and crevasses.
Bake the shepherd's pie until the top is barely golden, about 25 to 30 minutes. Remove from the oven, let cool slightly and serve.