Preheat your oven to 350°F and grease a 9x13-inch baking dish with butter. While it heats up, gather all your ingredients so you're not scrambling mid-recipe. This takes literally two minutes but saves so much stress when you're cooking.
Melt 1/4 cup butter in a large saucepan over medium heat until it's foamy and smells amazing. Sprinkle the flour over top and whisk constantly for about 2 minutes to create a roux. You want it to look like wet sand, not lumpy or burnt.
Slowly pour in the milk while whisking continuously to avoid lumps forming. This is where patience matters—don't just dump it all in at once. Keep whisking for about 3-4 minutes until the mixture thickens and coats the back of a spoon.
Stir in the cream of mushroom soup, garlic powder, black pepper, and dried thyme until everything's combined smoothly. The sauce should look creamy and uniform with no streaks of soup visible. Taste it and adjust the seasoning if you need to—this is your chance to get it perfect.
Add the shredded chicken, frozen green beans, and cheddar cheese to the sauce and fold everything together gently. Don't overmix or you'll break up the beans too much. The mixture should look cohesive but not mushy—everything should stay somewhat intact.
Pour the entire mixture into your prepared baking dish and smooth the top with a spatula. Sprinkle the French fried onions evenly over the top—don't pile them in one spot or they'll brown unevenly. My trick is using my fingers to scatter them so every bite gets some crunch.
Bake for 25-30 minutes until the casserole bubbles around the edges and the onions turn golden brown. When it's done, the top should be noticeably crunchy and the filling should be steaming hot. Let it rest for 3-5 minutes before serving so it sets up slightly and isn't runny on the plate.