What cooking method involves covering small food pieces with liquid and simmering?

The cooking method that involves covering small food pieces with liquid and simmering is stewing. This technique is particularly effective for infusing flavors into the ingredients, as the food cooks slowly in the liquid, allowing the tastes to meld together. Stewing is typically used for tougher cuts of meat or heartier vegetables, which benefit from prolonged cooking times to become tender. The key characteristic of stewing is the gentle heat and the fact that the food is partially submerged in the liquid, which not only helps in cooking but also in creating a rich, flavorful sauce or broth as the ingredients release their natural flavors during the cooking process.

In contrast, blanching is a quick cooking method used to partially cook food, often vegetables, by boiling them briefly and then plunging them into ice water. Frying involves cooking food in hot oil, resulting in a crispy exterior, while sautéing uses minimal oil or fat to cook food quickly at higher temperatures, typically in a pan over direct heat. These methods do not involve the prolonged simmering in liquid characteristic of stewing, making stewing the correct choice for this question.