Preheat oven to 375 degrees F.
Peel the potatoes and cut into quarters. Place in a good sized pot and cover with cold water. Set over HIGH heat, cover and bring to a boil. Once boiling, reduce heat to LOW and allow potatoes to simmer until tender when pierced with a fork, approximately 15 to 20 minutes.
Meanwhile, get started on the filling. Add olive oil to a 12-inch oven-proof skillet and place over MEDIUM heat. Add ground beef and cook, stirring to break up. Season with ½ teaspoon salt and ½ teaspoon freshly ground black pepper and continue to cook until meat is no longer pink. Drain grease and transfer cooked beef to a plate.
Add remaining olive oil to empty skillet and return to MEDIUM heat. Add onion and carrot and sauté until slightly softened, about 3 minutes. Add garlic and sauté for a minute or two until fragrant. Add tomato paste and stir well to combine with veggies. Add cooked ground beef back to the skillet and season with remaining salt, pepper, rosemary, thyme, and Worcestershire sauce. Reduce heat to MEDIUM-LOW and allow to simmer for 2 to 3 minutes.
Combine the beef broth with the cornstarch and add to the skillet. Cook and stir over MEDIUM heat for 2 minutes or until thickened. Stir in frozen peas and corn (no need to thaw) and allow to simmer for 2 to 3 minutes just until heated through. Remove skillet from heat.
When potatoes are fork tender, remove from heat, drain well and add the potatoes back to the warm pot. Place milk in the microwave for 30 seconds, just until warmed through. Use an electric hand mixer to mash the potatoes slightly. Add the warmed milk, sour cream, softened butter, and salt and continue to mash until smooth.
Dollop spoonfuls for mashed potatoes over the top of the filling and use the back of the spoon to spread it out evenly. Sprinkle with cheese. Transfer skillet to the preheated oven and bake for 20 to 23 minutes, until bubbling around edges. Turn oven to BROIL and watching closely to be sure it doesn't burn, continue to cook just until golden brown.
Remove skillet from oven and garnish with minced fresh parsley and fresh ground black pepper. Allow to sit for about 5 to 10 minutes before serving.