Basil Pesto Vinaigrette - what kind of vinegar?
They likely used white balsamic vinegar which is not cheap but has the kind of taste that sends people searching on the net ;) In character, it is sweeter than white wine, rice wine, and normal white vinegar and less acidic.

btw, you can easily make your awesome own pesto in your blender using fresh basil, pine nuts, and olive oil.  If you blanch the basil, it'll stay bright green and pretty for the life of it.