The Verdant Sprig is a component added by Roots. It has a 1/30 chance of being dropped when crops (anything that is an instance of BlockCrops) are broken. It is used for various spells.
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Verdant sprigs will drop at a 1/30 chance when harvesting fully-grown crops of all kinds. They have innate life force that persists after being harvested, so their uses often relate to bringing life to objects.