Add oil to a large skillet, heat to medium, saute mushrooms until tender and they begin to release moisture, approximately 5 minutes. Add minced garlic to mushrooms and continue to saute for one additional minute. Add cornstarch and stir to combine. Add broth and green beans, cook until liquid begins to thicken and green beans are slightly tender, approximately 10 minutes.
Stir milk into green bean mixture, pour into a 2 quart casserole dish. Add 1/2 cup shredded cheese and stir to combine. Bake until hot and bubbly, approximately 20 minutes. Sprinkle remaining cheddar cheese on top and bake an additional 8 to 10 minutes, or until cheese is melted.
Notes
If you plan to use the recipe for Baked Onion Rings, add half to the green bean mixture and evenly distribute the other half on top before baking.