3/8" shaft motor -> 20 tooth timing pulley (3GT (GT2-3M) Timing Belts)

If it was close enough to 8mm, see 3GT (GT2-3M) Timing Pulley - 20 Tooth - 9mm Belt - 8mm Clamp Bore - for other sizes you will need to source from 3rd party suppliers like McMaster or Small Mechanical Components: Precision Gears, Timing Belts, Gear Assemblies, Timing Belt Pulleys, Couplings, Bearings and much more - SDP/SI

 

By a lathe
buy tooling for it
learn to use it
buy more tooling (repeat these 2 lines for a while)
mount the pulley accurately
bore and ream to 3/8"
mount on motor

simple (-:

 

Thing is, if you build stuff, once you have a lathe you will use it often. I certainly cannot envision life without my lathe. Used it on Sunday to shorten some 3mm bolts for the 3D printer I am building. Yes, one could just grind the end off with a Dremel clone, I have 3 of those, but the lathe does such a nice job and much quieter.

but it was all a bit of a jest (-: you can just order the parts, quicker and cheaper.