Sending the stuck die to the manufacturer is easiest, but if you want to do it yourself:
Whichever method you use to remove that broken case, you have to be VERY careful NOT to scratch or damage the sizing die cavity!
1. Back off neck sizing plug and decapping pin stem. Remove both, if possible. That will make the following easier:
Use an oversize stainless steel bore brush and cleaning rod. Forcibly insert the brush into the broken shell, well into the neck portion of the case. Hold the die in a bench vise padded with wood blocks. Wiggle and try to pull it out.
If that doesn't work, try the following:
2. Clean and degrease the inside of the die cavity/broken shell case. Insert a coat hanger wire with the end bent into a "U".
Heat up both by dipping end of die (CAREFULLY!!!) into a pot of bullet casting lead. Be SURE to use pliers and protective clothing and eye protection!
When hot, use your ladle to pour the broken shellcase cavity BRIMFULL. Let cool.
Hold die in padded bench vise again. Grab coathanger and forcible pull the case out of the die.
HTH
John