To take an object (broom handle, flashlight, Oscar Award, etc) and forcibly apply it against a person's anus with the intent to humiliate that person. Recipient may/may not be fully clothed at time of "brooming".
"Stop being such a baby, man. It's not like your mom was raped... it was just some innocent rectal brooming."
To poke, prod, or otherwise attempt to insert the handle of a broom or mop (or any cylindrical object of the appropriate size, e.g., a flashlight) into the rectum.
This apparently is a hazing procedure that recently came to light in a story from Arizona in which two boys (aged 18 and 19 years old) were accused of performing "rectal brooming" on 18 middle school boys aged 11 to 15. Apparently, the victims' clothes remained on during the assualt. These charges were originally classified as felony sexual assualt, and later downgraded to a misdemeanor. The current spin is that the incidents were a hazing gone wrong. One of the boys charged is the son of a prominent politician and is a member of the Church of Latter Day Saints, giving this incident widespread recognition and debate.