There are repeating memes and reference regarding the love of banana and cookie of the doctor. Where did they come from?
The Tenth Doctor once said to Rose "Always bring a banana to a party", I believe this is where the meme originated. The doctor also replaced guns with bananas on two separate occasions to prevent someone from shooting someone else.
The Eleventh Doctor once tricked the Daleks into thinking a Jammie Dodger (a biscuit/cookie filled with jam) was a self-destruct button for the TARDIS.
According to the TARDIS wiki page on bananas, the meme goes back quite a while, pre-dating the new series.
Jo Grant brought a captive Ogron a banana. He did not comprehend her instructions to peel it. (TV: Frontier in Space)
On Space Station Chimera, the Sixth Doctor found a banana whilst searching his pockets for piece of wire. He gave the banana to Peri, who later started to eat it, but gave up when the sight of a dead Androgum made her feel sick. (TV: The Two Doctors)
The Fourth Doctor expressed a fondness for bannanas, once stopping an alien fleet with one. (COMIC: Death to the Doctor!)
So the banana thing might be a reference to the Third, Fourth and Sixth Doctor.