Start at the front end - ribbon mic.  Soft top end.  Run through a pre or front end hardware w/ transformers.  That too can roll off the top, soften the transients and thicken up the whole tone.
 
I have a $50 mxl ribbon that works magnificently on guitar amp.  And it is OK on vocal.  Run that through a WARM Audio WA12 pre (I haven't used the new Neveish one) in a small dampened room.  I bet you can get close.
 

A couple of free plugs that may help
 
https://klanghelm.com/contents/products/MJUCjr/MJUCjr.php
https://klanghelm.com/contents/products/IVGI/IVGI.php
 

What Jack said. If you use any reverb it would be a structural space or a Plate or spring. 
But the sound was a clean pure sound and good talent.