See first : Heat levels: high, medium, low, boiling and simmering
A roux is melted butter in which you cook the same amount of flour, for a minute or two. It is the base that thickens a béchamel, a gratin sauce, a blanquette, a velouté. White, you cook it just enough to remove the raw flour taste. Blond, you leave it a minute or two longer, to a biscuit colour, for more flavour.
Same weight of butter and flour, medium heat, and you stir all the time: a roux is not left alone, but it only takes two minutes.
40 g of butter and 40 g of flour thicken 500 ml of liquid for a coating sauce. For a thicker sauce, for a gratin or croquettes, 50 g of each.
Two to four minutes, without stopping stirring.
It browned or smelled burnt: start again, it is 40 g of butter and two minutes, and a burnt roux gives a bitter taste to the whole sauce. It makes lumps with the liquid: it is almost always because the liquid came too fast, whisk hard or run the sauce through an immersion blender, they disappear.
A ham and pasta gratin: the roux, the béchamel on top, and the oven does the rest.
Easy