Boil potatoes in salted water until tender, about 15 minutes. Drain potatoes and return to pot. Mash potatoes with cream cheese. Stir in milk and season with salt and pepper to taste.
Preheat oven to 350°F.
While potatoes boil, heat the butter in a medium skillet brown and crumble meat for 3 minutes, add onion and carrot and continue to cook until meat is cooked through and veggies have softened, about 5 minutes.
Stir in the flour and then broth and cook another 3 minutes or until sauce has thickened. Stir in peas, thyme, and season with salt and pepper.
Pour meat/vegetable mixture into a 1½ quart baking dish. Spoon potatoes evenly over meat and crosshatch with a fork.
Top with cheese if desired and bake for 30 minutes.