I have blogged about this in the past - the first time was in 2007 - it's how I clean my Pampered Chef Pizza Stones.
It's easy. I keep them in the oven when I set it to 'self-clean'.
They go in dark, they come out clean and beige. If they are heavily soiled or dark, I'll have to wipe the ash off with a paper towel.
No, really. That's all I do.
As a matter of fact, the photo above shows my stones - Pampered Chef Pizza Stones that were bought in 2005.
I've been cleaning them in my oven on 'self-clean' regularly since 2007.
It's now 2021.
When I first started to clean them this way in 2007 I'd have to season them again by making something a bit greasy but that was easily; I'd just bake buttery croissants them. That was usually enough to re-season.
(This is not how I'm telling you to clean yours; that's up to you. It's how I clean mine. All three of them. For the past 16+ years.)
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My stones literally live in the oven all the time. They stay in when I bake other items (usually) and they work as a drip pan of sorts as well, which is great. Because they are about 18 years old, they are well seasoned and turn a nice dark, almost black color very quickly even with just a couple uses. The are the beige stone color right out of the oven, but the darkness returns within a couple uses - again, because they are so well seasoned after so many years. When I first started to clean on self-clean back in 2007, I'd have to re-season them to get that non-stick awesomeness. Usually I'd just make something like canned, store-bought croissants on them as they were 'greasy' enough to season the pan for me for future uses. But after a few years, I didn't need to do anything with them after cleaning.
To clean them in between the deep cleanings, I just use the little plastic scraper to scrape them. Sometimes some really hot water but never soap.