Left Pic – Finger button broken, leaving the broken threaded part in the stem
Right Pic – Holding the valve in a valve lapping block so I can drill out broken piece

Left Pic – I’m using a left twist drill bit(it cuts opposite of a normal bit) to begin to drill out the broken piece
Right Pic – The advantage of the left twist drill is, sometimes, it will catch and spin out the broken piece, as it it did here.

Left & Right Pic – All out