Barbecue was a type of cooking.
The Second Doctor went back in time to prevent an earlier version of himself from speaking to a little boy, which had resulted in the boy getting hit by a car and having his legs damaged. Having averted that timeline, the Doctor, Jamie McCrimmon and Zoe Heriot later watched as the boy and his parents went to the beach for a barbecue. (PROSE: One Small Step...)
Sausages and burgers were foods common to barbecues, (TV: The Power of Three) as was barbecue sauce. (TV: Cyberwoman)
Other references
Jack Harkness claimed to Rose Tyler that a delta wave had the potential to "barbecue" one's head. (TV: The Parting of the Ways)