Add potatoes to a large pot of boiling water. Boil the potatoes until soft, 15-20 minutes.
Meanwhile, cook ground lamb (or ground beef) in a large saucepan over medium-high heat until browned, about 5 minutes. Add in onion and saute until onion is soft and translucent, about 5 to 7 minutes.
Add in 2 tablespoons butter and let fully melt before adding in the flour, stir until well mixed and let cook for 1-2 minutes. Pour in the beef broth and Worcestershire sauce and bring to a simmer. Add in frozen peas, carrots, corn, and thyme. Stir occasionally until the sauce thickens.
At this point the potatoes should be done. Drain and mash using either a potato masher or hand mixer. Mix in the butter, cream cheese, and salt until everything is melted.
Preheat oven to 350 degrees Fahrenheit. Lightly grease a 9x13 pan. Spread meat and vegetable mixture into the bottom of the pan. Top with a layer of mashed potatoes. Sprinkle cheddar cheese on top.
Bake in a 350 degree oven, uncovered, for about 15-20 minutes., until cheese is warm and bubbly.