1 large russet potato (3/4 pound), very thinly sliced
Preheat oven to 400 degrees. In a large skillet, heat 1 tablespoon butter over medium-high. Add onion and carrots and cook, stirring often, until onion is soft, 5 minutes. Season with salt and pepper and stir in tomato paste. Add meat and cook, breaking up with a wooden spoon, until almost cooked through, 3 minutes. Add thyme and beer and bring to a boil. Cook, stirring frequently, until slightly reduced, 2 minutes. Sprinkle flour over mixture and stir to combine. Add 1 cup water and cook until mixture thickens, about 2 minutes. Stir in peas and season with salt and pepper.
Transfer mixture to a 2-quart baking dish. Top with potatoes, overlapping slices. Season potatoes with salt and pepper and drizzle with 2 tablespoons butter. Bake until potatoes are browned around edges and tender when pierced with a knife, 40 to 45 minutes. Let cool 10 minutes before serving.