When I think of Brandon babysitting, of course I think about S1 and Melissa's baby Joy in One Man and a Baby. I completely forget he used to babysit Jessica Alba's baby in S8 too. Here's a cap of it, and I could swear there was an almost identical scene in One Man and a Baby - the same angle and the same way of holding a baby, just Brandon's face and clothes being different
But I can't find the cap. So, here's S8: