He/she is 'broad minded' means they are generally an open minded person.

"Broaden your mind" or "Broaden your horizons" are common idioms. "broadened mind" and "broad mind" are grammatically correct, but don't sound very natural and aren't used very often. It's more natural to say "open mind". "He reads often, so he has developed an open mind" "It's important to learn about other cultures to open your mind"

I think we use broad-minded to express our opinion that someone is not easily shocked. To be open-minded is more general, meaning someone who does not judge prematurely.