Some time ago when making some parts out of 316 stainless steel, l broke the tip off a 3/16" diameter centre drill (Slocumb bit). The broken bit was jammed in the bottom of the cone and as the part had already had a lot of machining time spent on it I was keen to reclaim it.
The method I used was very simple and did not even require me to take the job out of the chuck.
Using one of the thin abrasive disks in a Dremel type tool I ground a clearance slot (same width as broken tip) across the diameter the into the broken end of the centre drill leaving the conical cutting edges untouched.
I then used the same cutter to cut a bit deeper into the material until the broken tip had no metal l left around it (it fell out by itself).
Not an earth shattering revelation but it might prove useful one day.
Ian