The loan phrase à la is shortened from the French à la mode de, which translates literally to in the style of. Though in English we have dropped the mode de part, à la‘s definition retains the meaning of the French phrase, so à la is just a breezy, sometimes pretentious way of saying in the style of or in the manner of.
Some writers include the French grave accent over the a in à la, but English is never kind to these marks, and it is left off more often than not.
The phrase is colloquial, so it might be considered out of place in formal writing. Consider alternatives such as in the manner of and in the style of.
Examples
At least Sidney Nolan emerges in credit. His faux-naive paintings – à la Henri Rousseau – of the folkloric bushranger, Ned Kelly, are among the most celebrated in Australian art. [Telegraph]
The entire plot of “Downton” (and a lot of English literature, a la Jane Austen) turns on two English words that are foreign to Americans. [LA Times]
There is even a scene involving projectile vomiting, à la Saturday Night Live.[AV Club]
This is minimalist movie-making a la Hitchcock – designed to play out in a place both remote and constraining. [Sydney Morning Herald]