How now brown cow? is a cheerful alternative to asking “how are you?”.
It is often taught in elocution as a way of demonstrating the rounded vowel sound “ow” (aʊI).
A popular hypothesis behind the origin of the phrase goes back to 18th century Scotland, where “brown cow” was supposedly said as a slang expression for a barrel of beer. In this sense “how now brown cow?” would be used for asking another pint in the local pub.