How do I mount a Docker volume while using a Windows host?

It is possible the / is interpreted as an option by the CMD Windows shell.

Try first a docker-machine ssh default, in order to open an ssh session in your VM. From there try the docker run again: docker run -v /c/Users/phisch/dev/htdocs:/var/www phisch:dev

As commented by thaJeztah in issue 18290:

You could consider using docker-compose; docker-compose allows you to define bind-mounted volumes relative to the location of the docker-compose.yml file.
Using a docker-compose file allows you to specify all options needed to run your containers in a single file, which makes it ideal for sharing between team members (ie, just run docker-compose up -d will start all containers for the project with the right options).

This comment mentions a&dding a second /:

docker run -v //c/Users/phisch/dev/htdocs:`/var/www` phisch:dev

Even in the docker toolbox msys shell session, there are issues (like issue 282)

Pyetro notes in the comments:

In Windows, a double slash is needed at the beginning of the path to indicate the working directory.
Just to work with short path use like this:

docker run -v //$(PWD)/folder:/folder ...

After lengthy discussion, the issue was that /var/www had a folder in it.

Mounting /c/Users/phisch/dev/htdoc onto an empty folder does work, but might not give the expected result, as the default CMD apache2-foreground might still serve its content based on /var/www (which would not have htdocs content if that htdocs is mounted onto another folder).