Reading up on compost tea makes me think that it would be possible to make some out of brewing waste. Most of the compost tea recipes I find outline are some sort of fermentable sugar along with some other non-fermentable polysaccharides or proteins. All these seem like they already exist in the grains, hops and maybe adjuncts in beer waste.
The idea here is to take all the spent grains from mashing, along with all kettle waste and boil them for 20 - 45 minutes. This would solubilize most the residual sugars left over, as well as gelatinize some of the proteins from the grain. It would also isomerize more of the alpha acids that are left over from the late hop additions.
Once the boil is done, dump everything into a bucket with a large muslin-bag and let it come to room temperature. I guess it could be aerated while it’s cooling down as well. Then take a cup or 2 of compost along with a cup or 2 of healthy soil and let it sit overnight. Once there is decent fermentation going, take the muslin-bag out, strain though a paint-strainer and use.