Before you begin baking, mix together the beaten egg and vanilla. Stir in the raisins, and allow to soak in the egg mixture for an hour or two, stirring periodically.
Preheat oven to 350. In a small bowl, whisk together flour, baking powder, baking soda, and salt.
In a separate bowl, cream together the butter, sugars, and banana until combined. Add in the egg, vanilla, and raisin mixture. Gradually add in the flour mixture until thoroughly mixed. Stir in the oats. (Dough will not be very stiff.)
Drop dough by tablespoonfuls onto a baking sheet lined with parchment paper. Bake for 11-14 minutes until set and lightly brown. (mine only took 11) Let the cookies cool for about 5 minutes on the pan, then transfer to a wire rack to cool completely. Best if stored in the fridge.