What cooking style describes a moist omelette characterized by a slightly runny consistency?

The cooking style that describes a moist omelette characterized by a slightly runny consistency is known as "baveuse." This term specifically refers to the technique of cooking the omelette to a point where the inside remains soft and slightly undercooked, which gives it a creamy and velvety mouthfeel. The baveuse omelette strikes a balance between being set on the outside while still maintaining a moist and runny center, making it distinct from other types such as fluffy or dry omelettes.

In contrast, a fluffy omelette is typically whipped to incorporate air, resulting in a light and airy texture but not necessarily runny inside. A firm omelette is cooked long enough to result in a completely set filling, lacking any moistness or runniness. A dry omelette is overcooked and has lost all moisture, leading to a texture that is not desirable in the context of a baveuse. Thus, "baveuse" is the accurate term to describe this specific style of omelette cooking.