Pre-heat your oven to 400 degrees Fahrenheit. Set aside a 9x13 baking dish.
Bring a large pot of salted water to a boil. Add the green beans and cook for 5 minutes, stirring occasionally. While the beans are cooking, fill a large bowl or container with ice water. When the beans are done cooking, pour them into a colander to drain and then transfer them directly into the ice bath. Let them sit in the ice bath for a couple minutes so that they stop cooking and then pour them back into the colander to drain again. Set the beans aside to dry (I spread mine out a bit on paper towels and pat them dry).
In a small dish, stir together the flour, salt, and black pepper until well combined. Place the butter in a medium saucepan and bring over medium heat until melted. Add the minced garlic and stir, cooking for about a minute. Whisk the flour mixture into the butter and garlic until thoroughly combined. It will be thick like a paste. Cook for another minute.
Add the broth to the flour mixture a little at a time, whisking it together until smoothly combined. Add the half-and-half and whisk together. Allow the mixture to start bubbling and then reduce the heat to simmer, stirring occasionally, for 5-8 minutes until thickened.
Combine the green beans and the sauce, either in a separate mixing bowl or right in your casserole dish and stir to coat the beans with sauce. Spread the beans evenly across your 9x13 baking dish. Sprinkle the French fried onions evenly across the top of the beans and bake for 20 minutes. You may want to check halfway through to see if you need to cover the dish in aluminum foil so that the onions don’t get too toasty.