Jane was different from the other kids. While all the other kids were playing with fire, Jane played with ice. Now, Jane has grown up and is an accomplished scientist or engineer in your discipline of choice.
Jane never got along with Joe, and after an argument between them, Jane has decided to literally freeze their relationship, by completely freezing Joe's entire body. (In this case, we can take "freeze" to mean "reduce the temperature of the object in question to 273 kelvin or lower, and turn any liquids into their respective solid forms".) She realizes that this will probably get her into trouble with the authorities, but she's okay with that.
Both of them are ordinary adult humans without any superpowers. Jane has access to whatever equipment and facilities might reasonably be available to a scientist or engineer in your chosen discipline. The technique is not required to work (or not work) in any particular location; it just needs to work somewhere she can plausibly get Joe. (So no cheating by taking a trip to Titan, and the South Pole on Earth is probably stretching it.)
Joe does not need to survive the process, or perish from it. He is, however, not a willing participant.
Jane is allowed to work anywhere it's reasonable for someone with her credentials to be working, but it's a big bonus if she doesn't require the assistance of coworkers to pull this off, as said coworkers might not be as inclined as she is to deal with the legal backlash.
What can someone like Jane do in order to, in as little time as possible, freeze Joe? Roughly how long will the process take?
Magic not allowed; answers should conform to known sciences.