ajbilyk, it seems to be a pest rather than a disease. Read the above posts, and do the same. Can you find the pest?
A pest like this USUALLY has a life cycle like this:
Female lays eggs on or under the leaf surface.
Babies emerge and burrow in (if they were eggs on the surface) and start feeding in between the layers of leaf tissue. No pesticide will touch them.
They grow big enough and emerge.
Here the life cycle varies:
Might repeat the cycle for 2 or more generations each year.
Might burrow into a safe plant like under the soil to hibernate.
Other.
Control is usually aimed at preventing the females from laying eggs. Row covers are pretty good. Traps work on some pests, not on others, and you need to know what pest it is. Traps are usually baited with pheromones that are species specific. Repellents might work, but again, you need to know the name of the pest. Pesticide can work, but it needs to be applied several times through the egg laying period to kill the females when they land on the plant, before they lay eggs.
If you are into organic pest control, many people make a slurry (blender or food processor) of things like garlic, hot peppers, mint, lavender, marigold, or other pest repelling materials and spray it on susceptible plants. Since these pests seem to like fragrant plants like basil and mint, I would not include these.
Once you see the spots about the only thing you can do is to remove the affected leaves and destroy them so the pests are killed.
