YES! I DID IT AGAIN!
I knew it. Guys, I know how to get the Icecream:
You have to run for a split second. That way the Head Teacher will think it was an accident. She'll still punish you to make sure you don't do it again, but she'll also give you an ice cream to make up for it. Now to test it!
EDIT: I think it works the same way a Fully Chocolate Muffin does: give you unlimited stamina for 10 seconds, and then return it to normal.