Is there a global, persistent CMD history?

No, Windows command prompt history can't be saved when a session ends.

Not natively but check out: http://mridgers.github.io/clink/ , makes cmd.exe much more productive. Quoting features from the project page:

Powerful Bash-like line editing from GNU's Readline library.
Superior path completion (TAB).
Paste from clipboard (Ctrl-V).
Support for the completion of executables/commands, and environment variables.
Undo/Redo (Ctrl-_ or Ctrl-X, Ctrl-U)
Improved command line history.
Persists across sessions.
Searchable (Ctrl-R and Ctrl-S).
History expansion (e.g. !!, !<string>, and !$).
Scriptable completion using Lua.