Which cooking method involves using a small amount of fat over relatively high heat?

Sautéing is a cooking method that specifically involves using a small amount of fat, such as oil or butter, while cooking food at relatively high heat. This technique is primarily used to quickly cook smaller pieces of food, allowing them to develop a rich flavor and a desirable texture. The high heat helps to sear the ingredients, creating a savory exterior while retaining moisture inside. This method is commonly used for vegetables, meats, and seafood, making it a versatile technique in a chef's repertoire.

In contrast, baking utilizes dry heat in an oven and does not require added fat in the same way sautéing does. Steaming involves cooking food with vapor and does not use fat or high heat in the same manner, focusing instead on moisture. Grilling is a direct heat method but typically involves a larger surface area and does not specifically require the use of a small amount of fat over high heat as sautéing does. Therefore, sautéing is the precise method that matches the given description.