My parsely has white spots on its leaves. What are these spots? Is my plant sick? How can I treat it?
The plants around the parsely seem okay (rosemary, thyme, etc.), and I don't see (or can't find) any bugs.
This looks a lot like powdery mildew.
This is what powdery mildew looks like:
There are many options for treatment. To be honest though, I don't know if it is worth the trouble. If the parsley was meant for consumption, I'd throw it away. Otherwise I'd remove the infected leaves and isolate the plant and start treatment to prevent further spread.
I'd start here if you're looking for treatment.
~ Powdery mildew can spread to other plants If the powdery mildew is left untreated.