Cut the green beans into 1 1/2-inch pieces. Slice the mushrooms, finely chop the onion, and mince the garlic and set aside.

Bring a large pot of salted water to a boil. Once the water is boiling, add the green beans. Blanch until bright green, about 3 minutes. Drain the green beans in a colander and rinse with cold water.

Set a large pot over medium-high heat and add the butter. Once butter is melted, add the onions and mushrooms. Saute until mushrooms are browned and shrunken and onions are soft, 6-7 minutes. Add the garlic and thyme and cook until fragrant, about 30 seconds.

Sprinkle the flour over mushrooms and onions. Stir with a rubber spatula to coat. Slowly pour the chicken broth into the pot, whisking to dissolve flour. Pour in the half-and-half and season with the salt and black pepper.

Cook the sauce, whisking constantly, until it begins to bubble and thicken. Reduce heat to medium-low and allow sauce to simmer, whisking occasionally, until it is reduced by about a third, 5-7 minutes.

Add the green beans to pot and stir to coat with sauce. Pour green bean mixture into the prepared baking dish.

Bake the casserole on middle rack of oven for 15 minutes.

Sprinkle the french-fried onions in even layer over top. Continue baking until casserole is bubbling at edges, 5-10 minutes.

Check to see that casserole is done. Remove from oven or add time as needed.

Allow casserole to rest for 10-15 minutes before serving.