For Meat Filling:
Preheat Oven to 400 degrees.
Wash, peel, and cut potatoes to 1/2 inch pieces. Place the potatoes in a medium saucepan and fill with just enough water to cover them. Place over high heat and cover until boiling, once the water is boiling uncover and reduce heat and simmer until the potatoes are very soft. This should take about 10 to 15 minutes.
While the potatoes cook prepare the meat filling. Coat a sauté pan with the oil and warm over medium heat. Add onion and carrot to heated oil and cook about 3 to 4 minutes until they begin to change color. Add in the garlic and stir then add in the ground meat, salt, and pepper and let brown. Sprinkle the meat mixture with the flour and toss to coat. After about a minute add in tomato paste, broth, Worcestershire, and fresh spices. Bring to a boil reduce the heat to low, cover with lid, and simmer for 10 to 12 minutes until sauce is thickened. Meanwhile return to the potatoes.
Drain the potatoes and return to pan. Heat the half and half in the microwave about 35 seconds until just warm. Mash the hot potatoes then add the warm half and half, butter, salt and pepper. Mash until smooth and stir in egg yolk until well combined.
Add corn and peas into the meat and spread into an 11×7 glass dish. Top with the mashed potatoes. Place the glass dish on a parchment lined sheet pan and bake 25 minutes or until potatoes begin to brown. Let cool about 15 minutes and serve.