Looks like leaf miners from here.

Here on the Front Range one of my spinach vars has already bolted and I'm about to lose my most heat-tolerant var in the next couple days, we have spanakopita on the menu for next week.

Dan

Yes. Leafminers. Some make serpentine trails. You have the blotch-forming kind.

To manage them this year, keep an eagle eye on the spinach plot then, as soon as you see the beginning of a new blotch, squish that small area between your finger tips.

Then next year, plant in a different space and immediately protect with floating row cover, loosely bloused but tucked in along the edges. This avoids the insect which lays the small white eggs on the backsides of the leaves. The reason for the new site is that the insect spends part of its life in the soil.

Mine are getting infested with leaf miners right about now. Look for tiny, cylindrical white eggs laid parallel to each other in groups. Mine seem to favor non-savoyed cultivars.

Lots of folks hereabouts overwinter spinach. They leap out of the ground in the spring and you get lots of production before the critters start. But I usu only lose a few leaves and here not a big deal. And I agree that the savoyed vars seem to fare better.

Dan