In a large skillet or sauté pan, cook the ground beef over medium-high heat, breaking it apart as it browns. Once fully cooked, lower the heat to medium and add the diced onion and carrots. Stir together and cook for 8–10 minutes, stirring occasionally until the vegetables are softened. Season with salt and pepper to taste. Add in the frozen peas and stir, allowing them to cook for another minute.

Next, incorporate the minced garlic, flour, and tomato paste into the mixture. Stir well and cook for another minute until the flour is fully absorbed. Pour in the beef broth, Worcestershire sauce, thyme, and add the bay leaves. Stir everything together, bring the mixture to a gentle simmer, and then reduce the heat to low. Allow it to simmer uncovered for 8–10 minutes, stirring occasionally, until the sauce has thickened and thoroughly coats the meat and vegetables. Discard the bay leaves and spoon the mixture into a 9x13-inch casserole dish, spreading it evenly across the bottom. Set aside.

Preheat your oven to 425°F (220°C). Place the chopped potatoes in a large pot and cover them with salted cold water. Bring the pot to a boil over high heat with the lid on. Once boiling, cook the potatoes for about 5 minutes until fork-tender, then drain. Spread the drained potatoes on a clean, dry surface for about 5 minutes to let the steam escape, helping to avoid excess moisture.

Transfer the potatoes to a mixing bowl and mash until smooth. Stir in the light butter, skim milk, and about three-quarters of the shredded cheddar cheese, mashing until fully blended. Add salt and pepper to taste.

Spoon the mashed potatoes over the meat mixture in the casserole dish, spreading it evenly to cover. Sprinkle the remaining cheese on top. Place the casserole in the oven and bake for approximately 30 minutes, or until the pie is heated through and the peaks of the mashed potatoes begin to turn golden brown.