Preheat oven to 400°F.
In a large skillet heat 1 tbsp unsalted butter over medium-high heat. Add diced onion, carrots and celery and cook until the onion is soft and translucent, about 5-7 minutes.
Add minced meat and cook, breaking the meat with a wooden spoon, about 5-10 minutes or until the meat is slightly brown. When the meat starts sticking to the bottom of the pan, reduce heat to medium. Stir in the tomato paste and flour, cooking for 1-2 minutes.
Deglaze the pan with dark beer and bring to a simmer. Add dried thyme and ground garlic. Stir in Worcestershire sauce and enough water to cover the meat. Reduce heat to simmer and cook until reduced and thick - about 30 minutes.
Peel the potatoes and slice thinly into circles.
When the meat is reduced and thick, check for seasoning, stir in the frozen peas and transfer to the 12 by 9 inch baking dish. Top with potatoes, overlapping the slices. Season with salt and black pepper, drizzle with 2 tbsp melted butter.
Bake until the potatoes are brown on the edges and can be easily pierced with a fork, about 40-45 minutes. Cool for 10 minutes before serving. Sprinkle chopped fresh parsley.