Did anyone else notice how in Inside Out the "cool girl" looked a lot like Colette from Ratatouille? She also has brown eyes like Linguini. Could this actually be their daughter? Maybe Linguini and Colette moved to San Francisco so Linguini to train under someone. I know of at least 5 celebrity chefs that live in San Francisco, and Linguini did need to learn to become a good chef.
This could also explain the "cool girl's" behavior. She acts cool because her parents are famous chefs, but is actually really insecure (as displayed by her Emotions) because she feels like she's living in their shadow.
One other thing, in both Riley's classroom and outside during lunch, there was a boy in the crowd of kids that looked a lot like Linguini as a child. Perhaps the cool girl also had a brother?
Gotta love Disney/Pixar's easter eggs.