Heat olive oil in a large skillet over medium heat. Add chicken and cook for 5-7 minutes until browned. Remove and set aside.
In the same skillet, sauté onion and garlic for 3-4 minutes until translucent. Add mushrooms, carrots, and green beans, cooking for an additional 5 minutes.
In a bowl, whisk together chicken broth, heavy cream, and Dijon mustard. Pour over chicken and vegetables, stirring to combine.
Transfer mixture to a greased baking dish. Sprinkle cheddar cheese and breadcrumbs on top.
Bake in a preheated oven at 375°F for 25-30 minutes until bubbly and golden brown. Let cool for 5 minutes before serving.