Which method of cooking involves submerging food in hot oil?

The method of cooking that involves submerging food in hot oil is frying. This technique typically employs oil that is heated to a high temperature, creating a crisp and flavorful exterior while cooking the food quickly. The immersion in hot oil allows for even cooking and aids in the development of distinct textures and flavors that are characteristic of fried foods, such as a crunchy crust.

In contrast, grilling involves cooking food over direct heat, often from a flame or hot surface, and does not involve oil immersion. Sautéing is a method that cooks food quickly over a small amount of fat in a pan, typically at high heat, but it does not submerge the food in the fat. Baking uses dry heat in an oven, which does not involve oil or submersion. Thus, the defining aspects of frying—submersion in oil and high-temperature cooking—make it the correct answer.