Not a teacher.
Produced is the right word (as something is being made - organically in this instance).
Produce would refer to the item being made eg. the eggs, vegetables, grains etc. For example - 'Many eggs, vegetables and grains are organic produce'. Meaning that they are being made (or produced) by organic methods.
I think this is what you were getting confused over, please let me know if you need further assistance.
Student or Learner