My previous conversation with an employee at a Caribbean restaurant, it took less than two minutes:
Employee - 'Hello, your through to the Turtle Bay Restaurant'
Me - 'Hey, I was wondering what on your menu is vegan?'
Employee - ' Hi there, give me a second I will pull up our list....'
They then read out their options.
Another option is to use an eating out guide, there are several out there, and two of them are,