Step 1

Preheat the oven to 400 degrees F. Put the potatoes in a large saucepan, cover with cold water by 1 inch and season with salt. Bring to a boil, then reduce the heat and simmer until tender, 20 to 25 minutes.

Step 2

Meanwhile, heat the olive oil in a large skillet over medium heat. Add the leeks and season with 1/2 teaspoon salt. Cook, stirring, until the leeks are soft but not browned, about 8 minutes. Transfer half of the leeks to a large bowl and set aside.

Step 3

Add the beef and lamb to the skillet with the remaining leeks. Cook over medium heat, breaking up the meat, until no longer pink, about 6 minutes. Pour off any excess fat from the skillet; season the meat with 1/2 teaspoon salt and a few grinds of pepper.

Step 4

Stir the carrots, garlic, Worcestershire sauce and thyme into the meat. Clear a space in the middle of the skillet and add the tomato paste. Cook the tomato paste, stirring, until slightly darkened, about 1 minute, then stir into the meat mixture. Pour in the stout and simmer until slightly reduced, about 2 minutes. Add the broth and bring to a simmer.

Step 5

Cook, stirring, until the carrots are almost tender, about 5 minutes. Stir in the peas; reduce the heat to low and let simmer while you mash the potatoes.

Step 6

Drain the potatoes and let cool slightly. Transfer to the bowl with the reserved leeks; add the butter, half-and-half and 1/2 teaspoon salt and mash well. Stir in 1/2 cup cheddar.

Step 7

Spread the meat mixture in a 3-quart baking dish. Dollop the mashed potatoes on top, then spread with the back of a spoon. Sprinkle with the remaining 1/2 cup cheddar. Bake until bubbling around the edges and the topping is browned in spots, about 25 minutes. Let rest 10 minutes before serving.

Step 8

You can assemble any of these dishes up to 2 hours ahead. Cover and refrigerate, then add about 10 minutes to the baking time.