The cardboard will do the job of killing off the grass by providing a barrier and blocking out light.
The next ploy for our little team was to inoculate logs with shitake spores. We had cut the logs a month before so that they were not too green and sappy, but not too dry - providing perfect conditions for the spores to establish themselves.
First, Kim drilled holes at intervals along the length of the logs. Most types of wood can be used except for Eucalyptus, and for ease of moving should be cut to about a metre in length and be around 4" thick.
Hannah then used a special tool to inoculate the logs by inserting spores in to the drilled holes.
The holes were then sealed by Veronique using food grade wax (normally used to seal cheeses).
By controlling the fruiting in this way you can have groups of logs fruiting in rotation and be harvesting mushrooms throughout the summer. Sadly oyster mushrooms don't respond to being shocked and will only fruit when they're ready, but they can otherwise be grown in the same way.