Remove the ends of the green beans and chop into small, bite size pieces. In a small pot of boiling, salted water blanche the green beans until bright green (2-3 minutes). Remove from heat and strain.
In another pot heat a tablespoon of oil over medium heat and saute the garlic and onion until softened (2 minutes). Add in 2 tablespoons of butter. Once the butter is almost melted whisk in the flour. This will make a thick paste. Stir in the milk and green beans. Season with plenty of salt and pepper. This will look like a thick gravy with green beans in it. ????
Remove the stems from the mushrooms and rinse thoroughly. Pat dry. In a larger oven safe skillet (like a cast iron one) Heat 1 tablespoon of butter plus 1 tablespoon olive oil over medium heat. Cook the mushrooms, stem hole down, for a couple minutes. Flip and continue to cook for another couple of minutes.
Remove the pan from the heat and fill each mushroom with the green bean filling. Top with a little cheese and crushed french fried onions. Place the filled mushrooms back in the warm pan and bake in the oven at 375°F for about 8 minutes, until the cheese is bubbly and the onions look golden brown.
Remove from the oven. You can serve the mushrooms straight from the pan or remove them to a serving plate. They will be juicy, as the mushrooms release moisture as they cook.