I shouldn't be too surprised to find that some wood burners also garden!
I'm a fan of wood ashes on the garden - one is to adjust my slightly acidic pH from the low 6's to something around 6.5 or slightly above, the other is the trace minerals in the wood ash. Just think - if you are burning some oak from a 75 year old tree, those deep roots have been gathering minerals for that whole time and gathering them from forest soil, not worn out crop fields.
We all have our moisture meters
... I think that a pH meter can be just as necessary for a gardener. There's the model I have:
https://www.jungseed.com/P/51326/Digital+Ph+Meter
There are numerous meters on the market. Much like our moisture meters - the device needs to measure between two contacts. You'll see most pH meters with two "probes" that you stick into the soil. The model that I have only has 1 - so how does it work? The very tip is separated by a non-conductive section of plastic from the rest of the probe. So it looks like one, but is really two.
I put some of my wood ash on the garden and then stop at some point. After I till in Spring, I'll check with my meter and know how close I got. Then I'll either add some more in the coming year or not depending on if I'm in my desired pH range.
Another place to go with ash is your lawn. Most lawn soils are too acidic, so wood ash and or lime can really help the health of your lawn.
Of course all of this is based on knowing what your soil pH is.