also, it might just be because I’m english but I’ve never heard of having roux with breakfast - what do you have it with, if you don’t mind me asking?
The roux is just the base for the breakfast gravy. We do (American) biscuits and gravy for breakfast here. Usually sausage or some other form of white gravy.
So, you start by heating some fat. Maybe you're having bacon with breakfast (streaky bacon, since you're English), in which case you can use the fat left in the pan after making bacon. Other options are butter, oil, maybe some grease left from cooking sausage, if you're making sausage gravy. Other animal fats work too (forgetting breakfast for a moment, you can use drippings from a roast to make gravy for a dinner).
So you heat the fat (medium-low), then you add flour. In theory it's equal parts by weight, but I ain't weighing shit, especially when it's just leftover fat that's already in the pan -- I just eyeball it and sprinkle in one spoonful at a time, whisking it with a fork or a whisk until the liquid fat has been thickened and is approaching a paste-like consistency. You cook this mixture until it turns golden brown.
That's it. That's the roux.
Now if you're making gravy you can slowly add milk for a white gravy, at bit at a time so you don't get lumps. For a brown gravy you add broth (also you'd typically want to brown the roux a little darker than you would for a white gravy or sauce).
Creamy pasta sauce? Add milk (this gets you a bechamel sauce, which is a great starting point for mac and cheese), garlic, and perhaps some cheese.
Soup? Add broth and whatever other elements you're putting in the soup.
It's just two ingredients, but it's the stepping stone to many delicious things.
You can also use cornstarch instead of flour, but I'm not a fan of the more gelatinous consistency it produces.