Extract the Broken Bit from the Collet Assembly

What happens here

After removing the retaining components, the collet assembly with the broken bit can be seen. The narrator identifies a small ball bearing that holds the bit. To extract the broken bit, he places the collet assembly onto a vise with the broken bit facing down into a gap, ensuring it's supported but has space for the bit to exit. He then uses a punch and a hatchet (as he couldn't find his hammer) to repeatedly tap the broken bit out from the top. The repeated impacts eventually free the bit.

Goal: Remove the broken bit from the collet assembly.