Those are blotch leaf miners, a tiny larvae that feeds on the interior of the leaves. New foliage might be able to be protected with occasional applications of neem oil. Snip off the infested leaves and discard.

I am new to gardening myself and my basil was doing the same. I live in RI and watered every 2-3 days and it looked like I was leaving them in the sun to long but was told I was watering them to much. (Honestly I dk how people can tell.) What I did though and it has improved my plants a little is water every 2-3 days depending on the heat and I started putting them in areas where they had full sun for only 6-9 hrs a day. Once they bulked up a little I put them in brighter spots. This did not fix the problem completely but it did help a lot. Hope it helps you.

I just had to get rid of 7 basil plants and their soil due to Downey Mildew. The leaves starting turning a blotchy yellow with brown undersides with tiny spores. It's a relatively new development in the East since 2008. Check the underside of the leaves if they are normal, it could just be that they're getting too much rainy, cool weather.

I'd just pick off the affected leaves and dispose of them. Since basil is an annual it isn't worth expending much effort or money on saving it and I wouldn't use any pesticide on something I was going to eat. Especially since the larvae are inside the leave so contact products won't work and you'd have to reach for a systemic.