Baveuse is a French cooking term meaning moist, juicy, just a bit runny or undercooked.
It is most used to describe a desirable state of doneness for omelettes or baked custards.
Language Notes
“Baveuse” comes from the French verb “baver” which means to drool or slobber. The word is spelt “baveux”, when it is applied to masculine nouns such as “Pain baveux de la sorcière”, which is a bread with melted Raclette cheese in the middle.