Dear Vince,

This looks like leaf miner damage.  A small fly lays eggs in the leaf not on it.  The larva eats inside the leaf and makes what are called mines, hence the name leaf miner.  The larva changes into a pupae and emerges from the leaf and drops to the soil where it creates a cocoon and then emerges as an adult fly.  I am attaching a video that shows their life cycle: youtube.com/watch?v=lmu1G30Nltg  Life cycle of a leaf miner by Koppert Biologicals.

They are difficult to get rid of.  You can look for a small usually black worm in the leaves but it may have left already.  Bag the damaged leave and put in the garbage.  Disturb the soil around the plants if you find the cocoons, destroy them as well.  

Use pure Neem oil (find it online) and follow the directions.  You can drench the soil around the plants that are affected and it will kill most everything in the soil.  Spray it on the leaves both sides to kill the adults as they will open holes in the leaves and suck the juices out. You use as little as a teaspoon for complete effectiveness.  Follow the directions on the container.

Often there are only a few worms in the leaves.  You follow the directions above and your plants should come back.  If this is a really large amount of larva you may lose the plants.  

Disturbing the soil with your hands, drenching it with Neem and removing the leaves that are damaged are about all you can do unless you want to remove the plants as well.  

After doing all of that, you can cover the plants with row cover sold in most nurseries.  Bury the cover in the soil or make sure that there are not tiny holes for the flies to get through.  That will stop them from depositing the eggs in the plant leaves.  Here is a brief outline on the Leaf Miner.  https://extension.umn.edu/yard-and-garden-insects/leafminers

The pesticides mentioned with exception of Spinosad in the above link are not for organic use.  Since your plants are grown to be eaten, I would only use Neem or Spinosad.

If you have further questions, please contact us again.