When you get home from the range, spray the chamber & muzzle end of the barrel with a good penetrating oil (Note WD-40 is NOT a penetrating oil, it is a Water Displacement formulation, hence its name).
Let it sit for a day (unless it's hunting season, then hopefully a couple of hours will work)
Now, get a bore brush 1 or 2 sizes larger than your normal bore size. Try going in from the muzzle end & slowly push it down towards the chamber end. Go slowly. With any luck, the case should come out with the brush.
If that doesn't work, try going from the chamber end. Once you get past the mouth of the case. rotate the brush/rod. Now slowly retract the brush & hopefully, it will come out.
Either of those 2 methods have worked for me in 99% of the cases over the years.
Next resort is a normal brush with a patch wrapped around it. Try going in from the front or back.
And if those methods do not work, I have resorted to:
DANGER! DANGER! Chamber damage can occur!
Screw in a tap lightly in to the brass case, then tap on a cleaning rod at the muzzle end. Out pops the case with, hopefully, no threads showing on the outside of the case.
Now go buy a broken shell extractor.