Place the cubed potatoes in a large pot of salted water, bring to a boil, and cook for 15 minutes until they are fork-tender. Drain well, return them to the warm pot, and mash with the butter, milk, salt, and pepper until completely smooth.

While the potatoes cook, brown the ground beef, chopped onion, and diced carrots in a large skillet over medium-high heat for 8 minutes, breaking the meat apart until it is cooked through and the vegetables begin to soften.

Stir the tomato paste, dried thyme, and all-purpose flour into the meat mixture, cooking for about 1 minute until the raw flour smell disappears and the mixture becomes fragrant.

Gradually pour in the beef broth and Worcestershire sauce, stirring constantly to scrape up any browned bits from the bottom of the skillet. Bring to a gentle simmer for 10 minutes until the gravy has thickened into a glossy sauce.

Preheat your oven to 400°F (200°C). Transfer the savory beef mixture into a 9x13-inch baking dish, spreading it into an even layer, then gently spoon the mashed potatoes on top and smooth them with a spatula to cover the meat completely.

In a small bowl, toss together the grated cheddar cheese and panko breadcrumbs, then sprinkle this mixture evenly over the potato layer.

Bake for 25 minutes until the cheddar is bubbly and melted, and the breadcrumbs are a beautiful golden brown color.

Remove from the oven and let the pie rest for 10 minutes to set before slicing. Serve warm with your favorite seasonal roasted or steamed green vegetables.