Put potatoes in a large, heavy pan and add water so that there is at least one inch of water covering the potatoes. Cover the pan with a lid and bring to a boil, then uncover and reduce heat to medium or medium low to simmer. Cook until the potatoes fall apart and drain in a colander, then return to warm pot.

While the potatoes are cooking, heat the butter and cream in a microwave safe dish on 70% or 80% power for about 30-45 seconds until the butter is soft.

Mash the potatoes. Add the heated cream and butter and continue mashing. Season with salt and pepper to taste, add the egg yolk and set aside.

Preheat the oven to 400 degrees F.

In a large skillet, heat the olive oil over medium high heat. Once the oil shimmers, add the onion and carrots and saute until softened slightly, approximately 3 to 4 minutes.

Add the garlic and stir for about 30 seconds, then crumble the ground beef over the top of the carrot, onion and beef mixture.

Cook the beef until it's browned, then sprinkle the flour over the beef and mix to thoroughly combine. Add the tomato paste, Worcestershire sauce, rosemary, thyme and chicken broth and bring to a boil, then reduce heat to simmer until sauce is thick and shiny, about 10 minutes.

Add peas and corn and stir another 2-3 minutes until cooked through.

Place greased ramekins or cocottes on a large baking sheet lined with parchment paper. Spoon beef mixture into ramekins so that they are approximately 2/3rds full. Top with mashed potatoes, using a rubber spatula so that the potatoes reach all the way to the edges and create a seal over the beef mixture.

Bake in oven for approximately 15-20 minutes until tops are golden brown and slightly crusty. Remove from oven and let stand for 5-6 minutes, then serve piping hot.

Top with the mashed potatoes, starting around the edges to create a seal to prevent the mixture from bubbling up and smooth with a rubber spatula. Place on a parchment lined half sheet pan on the middle rack of the oven and bake for 25 minutes or just until the potatoes begin to brown. Remove to a cooling rack for at least 15 minutes before serving.