1. Preheat oven to 425°F.
2. Place cut potatoes in pot filled with cold water. Add a tablespoon of salt. Turn heat to high and cover slightly. Once boiling uncover and drop heat to medium-high. Cook until you can pierce potatoes easily with a fork, about 10-15 minutes.
3. While waiting for the potatoes to cook, prepare the filling. Heat the oil in a medium sauté pan over medium-high heat. Add the onions and carrots and cook until softened, about 5-6 minutes. Add garlic and thyme and stir.
4. Immediately add in the ground beef, 1 teaspoon salt and 1/2 teaspoon pepper. Stir occasionally until meat is cooked through, about 7-8 minutes. Drain excess fat.
5. To meat, add flour and tomato paste. Stir until incorporated and cook for 1-2 minutes. Stir in the beef broth and Worcestershire sauce.
6. Bring mixture to a boil, then reduce heat to a simmer, stirring occasionally until very thick, 2-3 minutes. Remove thyme sprigs.
7. Add defrosted corn and peas. Taste and season with salt and pepper, if needed.
8. Strain the cooked potatoes and place back into the pot. Cook over medium heat until the potatoes are dry, about 1-2 minutes. Take off heat.
9. Add butter and mash the potatoes. Once mashed, stir in heated milk. Quickly stir potatoes and add egg yolk, moving quickly to prevent cooking. Taste and season with more salt if needed.
10. In a 11 x 7 baking dish add meat mixture and spread evenly. Top with mashed potatoes starting at the corners working around the edge. This should seal in the meat for better chance of avoiding boil-overs. Use a fork and create fast swirly motions to fluff up potatoes.
11. Bake until potatoes are slightly browned, around 25 minutes.

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