Preheat your oven to 375°F.
In a skillet over medium heat, cook the lean ground beef until browned. Drain any excess fat if necessary and season with salt and pepper.
Add diced carrots, green peas, and sliced mushrooms to the skillet, and cook for about 5 minutes until the vegetables are tender.
Meanwhile, steam the cauliflower until very tender, about 8-10 minutes.
In a small bowl, lightly beat the egg and stir it into the beef and vegetable mixture to bind the filling slightly, cooking for an additional 2 minutes.
Mash the steamed cauliflower with a small amount of light butter, and season with salt and pepper to taste, until smooth and creamy.
Transfer the beef and vegetable mixture into an oven-safe dish, then layer the creamy cauliflower mash evenly on top.
Bake in the preheated oven for about 10-12 minutes until heated through and the top is lightly golden.
Remove from the oven, let it cool slightly, and serve.