Cover the potatoes with cold water in a large pot; season with salt and bring to a boil. Reduce heat to a simmer and cook until tender; 15-20 minutes
In the meantime, heat the olive oil in a large skillet over medium heat; stir in the onion and carrots. Season with salt and pepper. Cook, stirring, until tender, about 6 minutes.
Increase heat to medium-high and add in the lamb. Cook, breaking it up with a wooden spoon until no pink remains; about 5 minutes. Drain fat and season with 1/2 teaspoon kosher salt and a few grinds of pepper.
Stir in the garlic and thyme; cook until fragrant.
Make space in the center; add the tomato paste and cook for 1 minute. Stir in the Worcestershire and wine; simmer until skillet is nearly dry, about 2 minutes.
Add the beef broth and simmer until the mixture is saucy, 4-5 minutes.
Stir in 1/2 cup frozen peas.
Transfer to a greased 3-quart baking dish.
Drain the potatoes and return to pot; add the butter and half n half; mash well. Season with salt and pepper and add in the mustard, scallions, and cheddar cheese.
Spread the potatoes over the meat with the back of a spoon, then make ridges with the tines of a fork.
Bake at 425 degrees F until the toping is golden, about 20-25 minutes.
Let cool at least 10 minutes before serving (If you cut into it too soon, everything will collapse. It needs a little time to set.)
Eat and enjoy!
For helpful recipe tips, variations, make-ahead instructions, and storage, please refer to the full article.
Nutritional information given is an automatic calculation and can vary based on the exact products you use and any changes you make to the recipe. If these numbers are very important to you, I would recommend calculating them yourself.