For crying out loud, just listen to tester, just remove the dipstick tube, remove the broken dipstick, put the tube back in, and get a new dipstick. JB Weld indeed!
This is one of the few cases where I think JB Weld might be a pretty good answer if removing the dipstick isn't easy and cutting the tube is. JB Weld is heat resistant and wouldn't be under a lot of stress. I'd use a "collar" of pipe that has an inside diameter the same as the outside diameter of the dipstick tube and just use the JB Weld to hold the collar in place and prevent oil leakage.
However, I think that I personally would probably try to work a hook into the end of a thin wire to make it into a "pick". Slip the hook past the dipstick end if that is possible, turn the wire 90 degrees and lift the dipstick out.
Nothing wrong with Tester's answer either, if there is enough plastic on the end of the dipstick to work with and it is a variety of plastic that melts rather than burning.