Yes they do the barbeque on the forward deck next to the Trivoli Pool. This seems to be a "trademark" meal on NCL as we have seen the same type of food served on every ship that we have been on. They serve barbeque ribs, chicken, sausage, hot dogs, hamburgers and assorted salads, etc.
While we are on the subject of food, don't forget to try the "Blue Lagoon". This specialty restaurant is free and open 24 hours/day, although one of the waitresses told us that they do close for a few hours each night to clean. This restaurant serves all kinds of "snack/fast food" from Buffalo-styled chicken wings to Chinese food. I have to admit, coming from Buffalo, the wings were not really the original style but they were tasty none the less. One tip however, a single order of wings equals three pieces with some celery and blue cheese dressing. If you want more, tell the waitress to make it a double or triple order. We saw some people ordering a dozen at a time.
The other things on the menu at this location are: fried potato skins, hamburgers and fries, won ton soup (excellent), Singapore fried rice, shepherds pie, chef salad and assorted desserts. This is a small place with only about 8 tables located on deck 7. There are more tables located outside on the promenade deck, weather permitting. You do sit at the tables and give your order to the servers. The menus are on each table. It is very informal and very popular. Especially for late-night snacks and breakfasts.