How should I clean this mess at the bottom of my wok?
A patina is expected in this type of cookware.  Even the Le Creuset web site discusses it at this link:

http://www.lecreuset.co.uk/Help-Advice/Care--Use/Care--Use-Cast-Iron-Satin-Black-Enamel/

Don't try to remove it. It's the sign of a seasoned pan and is helping, not hurting. 

If you really feel the need to try to remove it, Le Creuset makes a cleaner for their enamel cookware you could try.  We've used it on our pots and it works quite well.

http://www.crateandbarrel.com/le-creuset-enameled-cast-iron-cookware-cleaner/s242309