Seeking advice on how to extract broken lug bolts

If your dead set against removing the flange or it is not drilled all the way thru then a plasma cutter on gouge setting will work. Start at the middle of the bolt and blast straight in. Slow and steady busts till you find the bottom of the hole.
Then cut one side to threads. And once cool you should be able to use a screw driver to spin out the broken parts. “Yes” the threads will get touched by the torch. Be gentle and do the least amount of damage as possible and clean up with a tap and die afterwards.