Add the all-purpose flour, whole-wheat flour, baking powder, baking soda, and salt to a bowl. Whisk for 20 seconds until well mixed. Set aside.
Melt 1 tablespoon of the butter in a saucepan over medium heat. Add the pumpkin purée and banana in the pan and use a silicone spatula to mash everything together. Continue stirring the mixture until the mash is reduced by half and darker in color. This can take 10-20 minutes — you just want all the water gone. Remove from the pan and allow to cool.
To a large bowl or stand mixer with the paddle attachment, add the remaining butter, white sugar, and brown sugar. Beat for 3-5 minutes on medium speed, scraping down the sides occasionally, until light and fluffy.
Add the eggs and vanilla. Beat for 5-10 minutes on medium-high speed, scraping down the sides every few minutes.
Add the dry ingredients (flour mixture). Use a silicone spatula to hand-mix, or combine everything in the stand mixer on the lowest speed just until you don’t see any more flour.
In a small bowl, mix the cinnamon and white sugar to make cinnamon sugar.
Scoop 2 heaping tablespoons (70 grams) of cookie dough and roll into a ball. Roll the ball in the cinnamon-sugar mixture until fully coated. Set on a baking tray or plate. Repeat this step until all the cookie dough is shaped and coated.
Wrap the tray/plate of coated cookie dough balls and let it rest in the refrigerator or freezer for 2 hours (at least 30 minutes).
When ready to bake your cookies, preheat the oven to 375°F. Bake the dough balls 2 inches apart on a cookie sheet for about 14 minutes. 12 minutes for fudgier cookies. 16 minutes for crunchier edges. Allow cookies to cool or enjoy hot with milk.