I've done this a few times with a phillips screwdriver, the adjusters I've had to deal with haven't been too tight, bit of pressure pressing down the screw driver and a gentle turn have been enough. A torx head hammered into the broken adjuster might have even more grip (but head will most likely be damaged). If there's a risk of adjuster being stuck, I'd start with soaking it in WD-40.
I've done this a few times with a phillips screwdriver, the adjusters I've had to deal with haven't been too tight, bit of pressure pressing down the screw driver and a gentle turn have been enough. A torx head hammered into the broken adjuster might have even more grip (but head will most likely be damaged). If there's a risk of adjuster being stuck, I'd start with soaking it in WD-40.