Preheat the oven to 350°F (175°C).
In a large skillet, sauté the onions and carrots until softened.
In a large mixing bowl, combine the corned beef, sautéed onions and carrots, sliced potatoes, cream of mushroom soup, Dijon mustard, garlic powder, salt, and pepper.
Grease a baking dish, then layer half of the potato mixture at the bottom.
Spread half of the shredded cheese over the potato mixture.
Repeat layering with the remaining potato mixture and cheese.
Cover with foil and bake for 30 minutes.
Remove the foil and bake for an additional 15 to 20 minutes until the cheese is bubbly and golden brown.
Allow to cool slightly before serving.