Does not seem to be related with avast.
Maybe they have time to look on it.
Please, go to folder \windows\minidump and send the newest (recent) .mdmp files for analysis. There is also C:\Windows\Memory.dmp file.
Better if you can compress (zip) them and add some information about the BSOD and the link for this thread.
Send an email to: vlk (at) avast.com
Or upload it to this anonymous ftp server:
ftp://ftp.asw.cz/incomingPost here what you've chosen.
Disable Automatic Restart:
System Properties > Advanced > [Startup and Recovery]Settings
Remove the checkmark from "Automatically Restart" in the System Failure section.
Maybe you need to create a manual dump: when the machine is in stalled state (or explorer crashed), hold down the rightmost CTRL key, and press the SCROLL LOCK key twice. This will cause a machine to 'blue-screen' and dump of memory will start.