2 TBS unsalted butter
1 large onion, chopped fine
2 medium carrots, peeled and chopped fine
2 pounds 85 percent lean ground beef
Salt and pepper
5 TBS all-purpose flour
1 TBS tomato paste
1/4 cup heavy cream
1 3/4 cups low-sodium chicken broth
3/4 cup beer (see note above)
2 TBS soy sauce
2 tsp minced fresh thyme leaves
1 cup frozen peas
2 1/2 pounds russet potatoes . peeled and cut into 2-inch pieces
2 TBS unsalted butter, melted
1/3 cup heavy cream, warmed
1 large egg, beaten
Salt and ground pepper
For the filling: Heat butter in large skillet over medium-high heat until foaming. Add onion and carrots and cook until soft, about 8 minutes. Add meat, 1/2 teaspoon salt, and 1/2 teaspoon pepper and cook, breaking up meat into small pieces with wooden spoon, until browned, about 12 minutes. Add flour and tomato paste and cook until paste begins to darken, about 1 minute.
Add cream and cook until it spatters, about 1 minute. Add broth, beer, soy sauce, and thyme and simmer over medium heat, stirring frequently, until mixture is thick but still saucy, 15 to 20 minutes. Remove from heat, stir in peas, adjust seasonings, and transfer to broiler safe 2-quart casserole dish.
For the topping: Adjust oven rack to upper-middle position and heat oven to 375°. Bring potatoes,1/2 teaspoon salt, and water to cover to boil in large saucepan over high heat. Reduce heat to medium-low and simmer until tender, 15 to 20 minutes. Drain potatoes, return to saucepan, and mash potatoes with butter and cream until smooth. Season with salt and pepper.
Spread potatoes over filling, using spatula to smooth top. Brush with egg and drag fork across top to make ridges. Bake until filling is bubbling, about 15 minutes. Turn on broiler and cook until top is golden brown, 3 to 5 minutes. Remove from oven and cool 10 minutes.
Make Ahead: Make the filling through step 2, but do not add the peas. Store in an airtight container in the refrigerator for up to two days. When ready to proceed, reheat the filling in a large saucepan, stir in the peas, and transfer to a broiler-safe 2-quart casserole. Proceed with the recipe from step 3.