Looks like sun and reflected heat from the rock mulch is causing stress. perhaps compounded by insufficient watering. IME, an organic mulch will be much better at holding in soil moisture as well as moderating soil temperatures - I'd get rid of the rocks :-)

FYI, it is NOT a disease!!

Thank you! I didn't think about the rocks reflecting the heat as it has been pretty hot. I'll have to move them elsewhere as I love peonies and want this little one to grow over the years.

I would be very careful with over mulching and over watering - plenty of peonies die that way. To me it looks more like a fungus than a water problem. Cut brown leaves and treat soil with fungicide. It s actually better to have rocks if it is a fungi problem.

I concur with Gardengal that it looks like leaf scorch, possibly due to excessive heat and insufficient watering, with the rock mulch intensifying those conditions. Like most plants, peonies like cool roots. An organic mulch would be more effective in maintaining more consistent soil temperature and moisture level. Just be sure to add only about 2" of organic mulch and keep it a few inches away from the crown and don't add too much.

Most diseases of peonies do not warrant the application of fungicides.

You can safely remove any severely browned leaves and dispose of them. On the off chance there is any disease there, do not add to your compost.

Alex is right about over mulching and over watering causing issues. You certainly don't want to put several inches of degradable mulch directly over your peonies. Some kind of wood based or pine straw mulch will work better to keep the roots cooler, though. Just make sure as has been stated above to keep the mulch back from the stems. I live in CO, we're considered high desert, and only water during the hottest parts of the summer, maybe once a week. A lot of my peonies look similar to yours right now! The ones planted in the last year typically go dormant earlier than those fully established. Once the leaves are mostly brown just cut the stem down to a few inches and leave it for the year. You won't cause your peony to put out new growth by watering this late in the summer but you certainly can cause root rot by overwatering. Peonies are perennial, they go dormant every late summer/fall. It's nerve racking to watch them wither the first few years--I still worry about mine every year even though I've been growing them now for decades! If you think of their habit more as a bulb that is perennial in your zone it's easier to understand their growth cycle.

If you are a gardener that fertilizes you can use an organic bulb fertilizer on your peonies. I'm not an expert on fertilizing but have used BulbTone on mine the last few springs and falls based on another respected peony grower's recommendation and I have had better and more blooms because of it. I think it's Hollingsworth's updates that recommended doing the same immediately after flowering as well. That's another thing I'd recommend--go onto the big online grower's sites--several have blogs that you can follow and almost all have lots of peony growing recommendations. You can learn a lot by reading all of that info--I typically go back through all of them during the winter when we're under several inches of snow and I'm missing summer! There is some conflicting information out there but everyone is the same on the basics for growing. If you're unsure about a recommendation it's typically best to consult experienced gardeners in your immediate area as things that work for me here in CO wouldn't work for someone further south with a lot of humidity, etc...