Turn the mulch over frequently, and spray with water occasionaly. Temperature will speed the process.
Turn, add a high nitrogen fertilizer (blood meal, etc), and water.
Kirk’s answer was good. It you add chemicals, fertilizer it will no longer be organic.
Another suggestion is to make sure the compost is in a dark container, either black or very dark gray. Preferably black. It absorbs the heat faster and speeds up the process. Also keep it in sunny area of yard.
Incorporate the plant waste into the soil. It will decompose faster then when lying on the surface.A compost pile or bin will also speed up the process but requires more work then on the garden composting.
Run a lawn mower over it and then till it into the soil.
That’s what farmers do to the corn stalks after harvest.
Cover the area with black plastic sheeting. We did this awhile back to an area with very poor hard clay soil. We then covered the plastic with mulch. The next time we planted in that area, the worms had turned the soil into very nice dark garden soil! I’d chop up everything first with the lawnmower if possible, as another answerer suggested.