Soak the first batch of pastries in the hot honey while you fry the second batch of briouats. Try to keep the briouats submerged by pushing down on them gently. When the next batch of briouats is almost ready to be removed from the oil, transfer the ones which have been soaking in honey to a strainer.
As you work with the remaining batches of briouats the volume of honey will decrease as it's absorbed by the pastries. You'll find that instead of submerging the pastries, you'll need to turn them over several times to ensure that they're getting coated as they soak. If the honey eventually seems to cool and thicken, heat it again to thin it. You can also add more honey to the pot if you find it easier to work that way.