As it's the new year I've updated my windows tweak scripts on github to reflect changes in Windows 10 1809.
Windows 10 1809 Information #
Microsoft Edge browser background process re-spawns the cortana searchui process if it gets killed.
It is possible to remove cortana after removing msedge.
Some windows updates reinstall Cortana & Edge (they can be removed again with scripts)
More information regarding the scripts can be found on github.