Prep your ingredients by washing, peeling, and dicing the potatoes, carrots, celery, and chopping the onion.
Cook the ground beef in a skillet with olive oil for 5-7 minutes until browned. Drain excess fat, then add the diced vegetables and seasonings. Cook for another 5 minutes.
Combine the beef and vegetable mixture with green beans, cream of mushroom soup, and milk in a bowl. Mix well and transfer to a greased baking dish. Top with cheddar cheese.
Bake at 350°F for 30 minutes covered, then uncover and bake for an additional 15-20 minutes until cheese is bubbly and golden brown.
Let the casserole cool for 5 minutes before serving.