There are any number of insects that will lay eggs like this - moths, whiteflies (although THEIR eggs are white), etc. I would do as Organoman suggest, just cut the leaves off and destroy them (I like stuffing them in a container of soapy water) but I'd also consider spraying the whole plant with some Spinosad which is organic and can be used up to harvest since you've got such a massive plant, it would be hard to find ALL the eggs and cut them off... but DO cut off the ones you can see!
Good luck!