For the Mashed Potatoes:

1. Preheat the oven to 400°F.
2. Peel and quarter the potatoes. Place in a medium pot with enough cold water to cover them by 1 inch. Transfer to the stovetop and bring to a boil over high heat. Reduce heat and simmer until the potatoes are tender, about 10-12 minutes.
3. Drain the potatoes and transfer to a large bowl. Mash with a handheld potato masher or ricer, so there are no lumps.
4. With a sturdy spoon or spatula, gently mix in the softened butter, sour cream, milk, salt, and pepper until smooth and creamy. Adjust the seasoning to taste with additional salt and pepper.

For the Meat and Vegetable Base:

1. Heat the olive oil in a large skillet over medium-high heat. Add the onion and 1/4 teaspoon of salt. Saute for 5 minutes, stirring occasionally, until translucent and slightly caramelized. Add the carrots and garlic and saute for another 3-5 minutes, stirring occasionally, until the carrots are just slightly softened.
2. Add the ground meat, the remaining salt, and the black pepper to the skillet. Cook the meat, stirring occasionally, until it’s browned but not yet cooked through, about 5-8 minutes.
3. Evenly sprinkle the flour over the meat and stir until completely incorporated. Add the tomato paste and continue cooking for another 2-3 minutes, stirring constantly.
4. Pour in the stock, red wine, and Worcestershire sauce to deglaze the pan, scraping the bottom of the skillet to release and incorporate any stuck-on browned bits. Stir in the thyme and 1 teaspoon parsley.
5. Reduce the heat to medium and simmer for 10 minutes, stirring occasionally, until the liquid reduces slightly and the mixture thickens.
6. Add the peas and corn and cook for an additional 5 minutes, stirring occasionally.
7. Adjust the seasoning with additional salt and pepper to taste and remove the skillet from the heat.

To Assemble and Bake:

1. Spread the meat and vegetable mixture in the bottom of a 2- or 2 1/2-quart ungreased casserole dish.
2. Gently spread the mashed potatoes over the meat and vegetable mixture in a smooth and even layer. Completely cover the bottom meat, being sure to spread the mashed potatoes until they touch the sides of the casserole dish.
3. Transfer the dish uncovered to the preheated oven. Bake for 25-30 minutes, until the mashed potatoes are lightly golden brown on top.
4. Remove the casserole from the oven and allow to cool for 10 minutes before garnishing with the remaining chopped parsley. Serve.