Peel and chop the russet potatoes, then place them in a medium saucepan. Cover with cold water and add 2 teaspoons of kosher salt. Bring to a boil over high heat, then cover and reduce to a simmer. Cook for 8 to 10 minutes, or until the potatoes are fork tender. Drain the potatoes and let them sit in the colander for 2 minutes to allow excess moisture to escape, then return them to the saucepan.

While the potatoes cook, finely dice the onion, mince the garlic, and chop the cremini mushrooms. Strip and chop the rosemary and thyme if using fresh herbs, or measure out dried herbs. Also, measure out tomato paste, flour, red wine, and broth. I like leaving the frozen vegetables in the freezer until just needed to keep them from getting soggy.

With the drained potatoes back in the saucepan, add 3 tablespoons of unsalted butter (reserving 1 tablespoon for later), some of the milk, sour cream or Greek yogurt, 3/4 teaspoon kosher salt, and 3/4 teaspoon black pepper. Mash until partly smooth, then add the remaining milk and continue mashing until fully smooth. Stir in the whisked egg until combined. The mashed potatoes should be thick but somewhat loose. Add more milk if needed to reach desired consistency. Cover and set aside.

Preheat the oven to 400°F. In a large oven-safe skillet over medium-high heat, melt 1 tablespoon of unsalted butter (omit if using fatty meat). Add the ground lamb or beef, crumbling it as it cooks. Season with 1/2 teaspoon kosher salt and 1/2 teaspoon black pepper. Once mostly cooked, add the diced onion, minced garlic, and chopped mushrooms. Sauté for about 5 minutes, until the vegetables are tender. Add the chopped thyme and rosemary, cooking for another minute until fragrant. Stir in the tomato paste and cook until it deepens in color, then add the flour and cook, stirring constantly, for another minute. Pour in the red wine, scraping up any browned bits, and simmer for 3 minutes until the alcohol cooks off. Add the broth and Worcestershire sauce, bring to a simmer, and cook for another 3 minutes until thickened. Stir in 3/4 to 1 teaspoon kosher salt and black pepper (to taste), then add the frozen peas and carrots and corn. Mix and spread the filling into an even layer.

If needed, transfer the filling to a baking dish. Spoon the mashed potatoes (from Step 3) evenly over the filling, spreading all the way to the edges to seal. Melt the reserved 1 tablespoon of butter and drizzle over the top of the potatoes. Bake in the oven for 15 to 20 minutes, or until the filling is bubbling at the edges. If you'd like a crispier, more golden potato topping, broil for 1 to 3 minutes until lightly browned—be sure to watch carefully! I always find that a little time under the broiler makes the top extra delicious.

Remove the pie from the oven and let it rest for 15 minutes before serving; this helps the filling set. Garnish with chopped fresh parsley. Scoop portions onto plates or serve family-style at the table.