Eggs on spinach
Good detective work. You’re correct! Those are eggs of leafminers. Squish them on sight, and then look for more eggs.
Leafminers feed inside the leaf and make either serpentine trails or large blotches. You can manage these pests for the rest of this season by regularly scheduling your search-and-destroy missions.
But next time you plant, choose a different area and then immediately cover the seeds, seedlings, or transplants with row cover, a non-woven “fabric” you can obtain at local garden centers. (An alternate choice is bridal tulle; it’s inexpensive and it can be cut to whatever length you need.). The reason it’s best to use a different site next time is that leafminers spend part of their life in the soil. Whatever your choice, loosely blouse the fabric to allow growing space and also anchor the cover at the perimeter to thwart the adult leafminer flies. Use a heavy object such as a board or pole, or even soil.See “Leafminers” http://www.ipm.ucdavis.edu/PMG/GARDEN/VEGES/PESTS/vegleafminers.html and “How to Install a Floating Row Cover” http://cru.cahe.wsu.edu/CEPublications/FS089E/FS089E.pdf