AFAIK you can establish an LLC on H1B, but you cannot be employed by it, unless your H1B is sponsored by that LLC...
Once your LLC has employees/revenue and can convince INS of LLC being legitimate ongoing business and not a shell to get you work authorization, you can have your LLC sponsor you for a work authorization.
Potential workaround: Don't draw a salary from your LLC. Hire contractors to do most of the work and pay them from LLC. Travel to foreign destinations time to time and classify them as business trips for 'working for LLC'.