Rough up the plastic, fill it with jbweld and stick a flat head screw driver in it.

After it cures, just turn it out like normal.

 

That is a great idea also.

Warming it up may help. I expect the o-ring seal is stuck on the metal part. Mine is always tight to get off cold or hot.

 

And get whats left of that o ring out of there before you do anything!

 

Internal pipe wrench.

 

Is that part of the dipstick down inside?

 

Looks like just the top cap broke off leaving the threads and dipstick in the top of the transmission/oil case. I think the JB Weld idea would work well with minimum cost/effort.

 

The internal pipe extractor tool @Chopper Man linked works very well and is pretty darn cheap. It's a handy tool to have around for many things.

That said, if you're careful you likely can rotate it out using a punch and a hammer. Just don't damage the metal housing doing that.

Once you get your replacement dipstick, I'd recommend spraying it with silicone spray, just to help keep it from sticking. I don't know what it is about Harley dipsticks, but they do seem to love sticking themselves in place. The silicone spray helps keep that from being so obnoxious.

 

Something I never thought of ... Just might do the trick

 

It looks like the engine oil dip stick for an unknown year and model.
It is unknown if it a factory original part, some aftermarket item or perhaps an accessory item.
It looks like the TOP/CAP part separated from bottom part.
It is unknown if it is an aftermarket or accessory product that might have a temperature gauge.
It is unknown if the secondary part is loose and has the possibility of falling deep into the pan.

If it is the plastic factory screw in kind of dipstick that has disengaged from top handle then perhaps just using some needle nose pliers OPENED on inside of tube portion to tighten plier legs against inside walls while turning would work to unscrew.
Covering each leg of opened needle nose pliers with some oil line or fuel hose might get you some more grip.
Just have a plan so nothing is dropped inside.
If you are going to lubricate with a few drops the junction of plastic to motor then might as well use the same engine oil to avoid contamination.
For heating that area of motor a hair dryer works and is more pin point to area of concern and there is less chance of burning your hands with hot motor while working in that area.

 

I got it out what I did was taking a 19 millimeter socket inserted it into the opening hammered it down lightly and then used a extension and ratchet and got it out and then broke the bottom of dipstick pn the ground then I got the socket out