Place peeled, cubed Yukon Gold potatoes into a large pot and cover with cold water by 1 inch. Add 1 teaspoon of sea salt. Bring to a boil over high heat, then reduce heat to medium-low and simmer for 15 to 18 minutes until completely fork-tender.
Drain potatoes thoroughly in a colander, then return to the hot pot. Add 3 tablespoons of softened butter, warm milk (or cream), garlic powder, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Mash thoroughly with a potato masher until creamy and smooth. Set aside.
Preheat oven to 400°F (200°C) with rack in the middle position.
Heat 1 tablespoon olive oil in a large 12-inch cast iron skillet or deep oven-safe pan over medium-high heat. Add ground beef and cook, breaking it into small crumbles with a wooden spoon, for 6 to 8 minutes until thoroughly browned. Drain off any excess fat if needed.
Add finely diced onion and carrots to the beef. Sauté for 4 to 5 minutes until onions are translucent and carrots begin to soften. Stir in minced garlic and cook for 1 minute until fragrant.
Add tomato paste and flour to the skillet. Stir constantly for 1 minute to coat the meat and vegetables, cooking off raw flour flavor.
Slowly pour in beef broth and Worcestershire sauce while stirring. Add fresh thyme, rosemary, remaining salt, and black pepper. Bring to a gentle boil, then reduce heat to low and simmer for 5 minutes until the gravy thickens into a rich, glossy sauce. Fold in the thawed green peas.
Level the beef filling in the skillet (or transfer into a 9x13-inch ceramic baking dish). Spoon the mashed potatoes over the top, spreading gently with an offset spatula to seal the edges completely.
Use the back of a fork to create textured peaks and ridges across the entire surface of the mashed potatoes. Dot the top with the remaining 1 tablespoon of butter cut into tiny bits.
Bake at 400°F (200°C) for 25 minutes until the edges are vigorously bubbling. Turn the oven to broil on high for 3 to 4 minutes until the potato peaks turn deeply golden-brown and crispy. Remove from oven, let rest for 10 minutes, garnish with fresh parsley, and serve warm!