Thicken your sauces and stews without worrying about burning flour
Growing up in Alabama, I knew that the hardest part of making gumbo was getting the roux right. Add as many tasty ingredients as you want, but if you don't have that essential binder, it'll be soup, not gumbo. Roux was intimidating to me. I knew burning it was bad. I knew that if I was making gumbo, I was also moving around 50 things at once in the kitchen, and burning it was also easy to do.
So when it was sauce day in the culinary program I'm in, I paid close attention to the section on roux, and what I learned was a revelation: There is absolutely no good reason to make your roux at the same time as your sauce and meat and whatever else you have going on. You can make roux ahead of time, put it in the refrigerator or even freeze it, and use it whenever you want to thicken sauces and stews.
First, a reminder on what roux is. It's a mixture of roughly equal amounts of flour and fat, usually oil or butter, that you combine and cook until it begins to color. You can have a lighter roux for lighter sauce like a béchamel and a darker one for darker sauces, like for gumbo. Basically you want to make sure the raw flour taste is gone for a lighter roux, and that it's a nice golden brown or even brown-brown for a darker roux. You have to keep an eye on it the whole time and whisk constantly because once it starts to take on color, things can progress rapidly and suddenly you've burned the whole thing and need to start over.
But there is nothing that says that you can't make a batch of roux well ahead of time and keep it for when you need it. In fact, that's what we do in class—break off a chunk from a quart container in the refrigerator and add it to a simmering sauce to thicken it. (You can also thicken sauces uses beurre manie, which is just combining equal parts soft butter and flour until it forms a kind of dough, which is a neat trick and also means you don't have the hassle of cooking the flour. Or you can roast flour in the oven and then combine it with butter! The possibilities, I tell you).
The only thing that you want to make very sure of when you're adding a roux or a beurre manie to thicken your suace—or even a cornstarch slurry—is that you have a temperature differential going. You can add cold roux to simmering stock, but if you add warm roux to the stock, the sauce will get lumpy. That's a useful thing to know for everything, but particularly when you're making gravy.