The immersion technique described above is recommended by eco-minded professionals who don't like throwing away organic matter.
Yes, we have a "ferti-butt" to create liquid feed from anything that doesn't go on a fire. We throw in all sorts of stuff like the daggy wool from the sheep botties and various pernicious weeds. However, with a large garden and a wood burning stove there is a merit order for treating arisings:
Soft stuff/not pernicious = compost. Two large heaps, each rotted for current year + next year (when we grow squashes and courgettes directly on the rotting heap)
Straightish sticks = shredder, with shreddings used on the veg patch paths
Twisty sticks/bramble/pernicious stuff = fire. Ash goes on veg patch.
Decent branches = firewood for wood burning stove. Ash goes on veg patch.
Travelling religion salemen = fire. Ash is jumped on and encased in concrete before sending to a deep underground repository for a million years.
Nothing that originated in the garden generally leaves site, although we have the space to deal with this. Everything is a resource.