Measure out all the mashed potato ingredients (butter, milk, sour cream or yogurt, salt, pepper, and beaten egg) so they are ready to use. Reserve 1 tablespoon of the butter in a small bowl for finishing the top.

Place the peeled and chopped potatoes in a medium saucepan, add cold water to just cover, and stir in the 2 teaspoons of kosher salt. Cover and bring to a boil, then remove the lid and lower the heat to a simmer. Cook for 8 to 10 minutes, until fork-tender, then drain well and let the potatoes sit in the colander for 2 minutes. Return them to the saucepan.

While the potatoes cook, prep the filling vegetables: chop the onion, mince the garlic, slice the mushrooms, and chop the thyme and rosemary. Measure the tomato paste, flour, broth, and wine, but keep the frozen peas, carrots, and corn in the freezer until you need them.

Returning to the drained potatoes, add 3 tablespoons of the butter, about half the milk, the sour cream or yogurt, 3/4 teaspoon kosher salt, and the black pepper. Mash until partly smooth, then add the remaining milk and mash until creamy. Gently stir in the beaten egg; the potatoes should be thick but slightly loose because they will firm up in the oven. Add an extra tablespoon or two of milk if needed, cover, and set aside.

Preheat your oven to 400°F.

Heat a 12-inch oven-safe skillet with high sides over medium-high heat (a cast iron skillet works well). If you prefer, use a regular skillet and transfer the filling to a casserole dish later. Once hot, melt 1 tablespoon of butter in the pan, unless your ground meat is fatty. Add the ground lamb or beef, breaking it into small crumbles, and season with 1/2 teaspoon each of kosher salt and black pepper.

When the meat is mostly browned, stir in the onion, garlic, and mushrooms and sauté for about 5 minutes, until the vegetables are tender. Add the chopped thyme and rosemary and cook for 1 minute until fragrant. If you used a fatty meat and there is excess grease, drain all but 1 to 2 tablespoons. Stir in the tomato paste and cook for 1 minute until it darkens, then sprinkle in the flour and cook for 1 minute, stirring constantly.

Pour in the red wine and red wine vinegar, and use a wooden spoon to scrape up the browned bits from the bottom of the pan. Let the liquid come to a simmer and cook for 3 minutes, until it has reduced and the sharp alcohol aroma is gone.

Add the beef broth and Worcestershire sauce, bring to a simmer, and cook for about 3 minutes, until the liquid thickens enough that it holds its shape briefly when a spoon is dragged through. Season with 3/4 to 1 teaspoon each of salt and pepper, taste, and adjust. Fold in the frozen peas, carrots, and corn, then spread the filling into an even layer. If you are using a separate baking dish, transfer the filling to that dish now.

Spoon the mashed potatoes over the filling, using an ice cream scoop if you like for even portions, and spread them to the edges with the back of a spoon. Melt the reserved 1 tablespoon of butter and drizzle it over the potatoes.

Bake for 15 to 20 minutes, until the filling is bubbling around the edges and the potato top is set.

If the potatoes are not browned enough, switch the oven to broil and cook for 1 to 3 minutes, just until the top is golden with a few charred spots. Keep a close eye on it to prevent burning.

Let the shepherd's pie rest for 15 minutes before serving.

Garnish with chopped fresh parsley if you like.

Scoop portions onto plates with a serving spoon. For a crowd, place the skillet or baking dish in the center of the table so guests can serve themselves. This hearty meal stands alone nicely, though a simple green salad is a great way to lighten it up.

Leftovers reheat well, though they lose a little sauce. Cool the pie completely before storing in airtight containers, keeping the potato layer intact in one even layer. Refrigerate for up to 1 week and reheat gently in the microwave.