The act of continuously cutting a piece of food in half so it appears the leftover half is for others. For example, a cookie is split in half and eaten, then the remaining half is split in half again and one half is eaten. The process is repeated until half of a crumb remains.
In a sentence, "Hey, stop Bijeeing that cookie! We don't want to eat your leftovers."
"I don't want to look like a pig, so I'll just Bijee this piece of cake."