On Sippuray Sumsum, Noah and Brosh were assistants in the workshop of Jewish handyman Tzachi. Tzachi and his Arab neighbor, Ibtisam, taught their young Muppet friends life lessons by telling them stories. 
In 2012, Brosh was removed from the series, and was replaced with Elmo.
In the book The Count's Hanukkah Countdown, Brosh has an Aunt Sara and Uncle Joe. They have twins, Sam and Sadie.
Sesame Workshop description
Brosh is a seven-year-old character with orange fur and red hair. He is responsible to a fault and loves order. His day is run according to a strict schedule that he expects others to follow too. Along with this love of structure comes a real competitiveness. Brosh likes to win—losing just is not part of his plan. But under all of this is a terribly sweet, sensitive, and insecure little guy. Brosh loves making lists and hates messes, bugs, and sticky things. He adores Noah, Tzachi, and Ibtisam, and would do almost anything for them.