Alton Brown Shepherd's pie is a very popular dish in the US. It is very easy to make and is a good alternative to regular pies. Shepherd's pie is a great dish for a family dinner.
Preheat the oven to 400°F. Peel the potatoes and dice them into 1/2-inch pieces.
Place the potatoes in a medium saucepan and cover them with cold water. Turn the heat to high, cover, and boil the potatoes. Remove the cover, reduce the heat to a simmer, and cook for about 10 to 15 minutes.
In an 11-inch saute pan, heat the oil until it is shimmering. Saute the carrots and onion until they begin to take on color, 3 to 4 minutes.
Stir in the garlic. Add the meat, salt, and pepper, and cook for approximately 3 minutes, until it is browned and cooked through.
Sprinkle the flour over the meat, toss to coat, and cook for one more minute. Stir in the tomato paste, broth, Worcestershire sauce, rosemary, and thyme.
Bring to a boil, then reduce the heat to low, cover, and simmer slowly until the sauce has thickened slightly about 10 to 12 minutes.
In the meantime, heat the butter and half-and-half in a microwave-safe container for about 35 seconds, or until hot.
Return the potatoes to the saucepan after draining. Mash the potatoes, then stir in the hot half-and-half mixture, along with salt and pepper. Mash until smooth, then stir in the egg yolk.
Combine the corn and peas with the meat mixture and spread evenly in a 7-by-11-inch glass baking dish. Add the mashed potatoes to the top, starting at the edges to create a seal so that the mixture doesn't bubble over. Smooth the top with a rubber spatula.
Place on a half sheet pan lined with parchment paper on the middle rack of the oven and bake for about 25 minutes, or until the potatoes are golden brown.
Remove from the oven and let cool on a cooling rack for at least 15 minutes before serving. Serve and enjoy!