Which cooking method involves cooking food slowly in liquid over low heat?

The cooking method that involves cooking food slowly in liquid over low heat is braising. This technique is particularly effective for tougher cuts of meat that benefit from long, slow cooking to become tender and flavorful. Braising typically starts with browning the food in fat, which adds depth to the flavor, and then the food is cooked covered in a small amount of liquid, allowing the food to simmer gently. This method not only breaks down connective tissues in the meat but also infuses it with the flavors of the liquid and any aromatic ingredients used.

Other methods listed, such as sautéing, grilling, and frying, operate at higher heat levels or require different techniques and do not encapsulate the essence of slow cooking in liquid. Sautéing involves cooking food quickly over high heat in a small amount of fat, grilling usually involves cooking food at high heat directly over a flame, and frying immerses food in hot oil to achieve a crispy exterior. These distinctions clarify why braising is the correct answer in this context.