Final answer:
A brown roux is cooked longer and has a rich brown color, while a white roux is cooked briefly and is pale in color. White roux is used for delicate flavors, while brown roux adds a deeper, nutty flavor. Examples include bechamel sauce with white roux and espagnole sauce with brown roux.
Step-by-step explanation:
In culinary arts, a roux is a mixture of fat (usually butter) and flour that is used to thicken sauces, soups, and stews. The main difference between a brown roux and a white roux is the cooking time and color. A white roux is cooked briefly until it just begins to take on color, while a brown roux is cooked for a longer period of time until it becomes a rich brown shade.
A white roux is typically used in dishes where a delicate flavor is desired, such as cream sauces and some soups. A brown roux, on the other hand, has a nutty flavor and is used in dishes that require a deeper, more complex flavor, such as gumbo or gravy.
For example, when making a bechamel sauce, a white roux would be used as the base, while a brown roux would be used as the base for an espagnole sauce.