bsod playing eve online. IRQ/KMODE not handled

Looks like a hardware issue, or at least not a driver issue, thank you for running driver verifier :) Unfortunately I cannot tell what may be the cause so I would suggest to start with a memory test.

Diagnostic Test

 RAM TEST

Run MemTest86+ to analyse your RAM. MemTest86+ - Test RAM - Windows 10 Forums

   Note

MemTest86+ needs to be run for at least 8 complete passes for conclusive results. Set it running before you go to bed and leave it overnight. We're looking for zero errors here. Even a single error will indicate RAM failure.

Make a photo of the result and post it.

Addition:
If errors show up you can stop the test, remove all sticks but 1 and test this single stick in each slot for 8 passes or until errors show, switch sticks and repeat.
If errors show up and you see them a lot later, no problem, the errors don't affect the test.

Please fill in your system specs

Please follow this tutorial and download the tool. The tool will give you detailed information about your system specs, please fill in your system specs more completely including PSU, cooling and other used stuff like mouse, keyboard, monitor, case, etc.
The PSU, cooling and other stuff are NOT mentioned in the tool.

In the left corner below in your post you find 'My System Specs'. After clicking it you can find a link a little below that says 'Update your System Spec', click on this link to get to the page where you can fill in your system specs.

Could you tell me how you get the idea of the CPU as a possible cause please (not telling it's wrong, just like to know how you get to it :))

A BIOS update could help (depending on the changes though)