Place peeled, cubed Yukon gold potatoes into a large pot of salted water. Bring to a rolling boil and cook for 15 to 18 minutes until fork-tender. Drain thoroughly and return to the hot pot. Mash with melted butter, sour cream, warm milk, garlic powder, sea salt, egg yolk, and half of the grated cheddar until smooth, fluffy, and creamy.

Preheat oven to 400°F (200°C). In a 12-inch oven-safe cast iron skillet or deep Dutch oven over medium-high heat, brown the ground beef for 6 to 8 minutes, breaking it into small crumbles until no pink remains. Spoon out excess grease, leaving 1 tablespoon in the skillet. Add diced onion, carrots, and celery; cook for 5 minutes until softened. Stir in minced garlic and cook for 1 minute.

Stir in tomato paste and flour, cooking for 2 minutes to eliminate raw flour taste. Pour in beef bone broth, Worcestershire sauce, minced rosemary, and thyme. Bring to a simmer, scraping up all browned fond from the bottom of the skillet. Reduce heat to medium-low and simmer for 8 minutes until gravy thickens into a glossy sauce. Fold in frozen peas.

Spoon the mashed potatoes over the beef filling. Use the back of a spoon or spatula to spread evenly to the pan edges, sealing in the gravy. Run the tines of a fork across the top to create diagonal textural peaks. Sprinkle remaining sharp cheddar over top.

Bake uncovered at 400°F (200°C) for 22 to 25 minutes until the beef gravy is bubbling around the edges. Turn on the broiler for the final 2 minutes to get deep golden-brown, crispy potato ridges. Rest for 10 minutes before scooping into bowls.