Preheat the oven to 350 degrees and line some baking sheets with parchment paper.
In a large mixing bowl and using a hand or stand mixer, beat butter and sugar till it is light and fluffy, about 4-5 minutes. Using a spatula, scrape the sides of the bowl, bringing the butter and sugar mixture back to the middle. Add the egg, egg white, and vanilla, then continue beating until combined.
In a medium-size bowl, mix the flour, baking powder, and salt to combine. Sift the flour mixture into the wet ingredients and stir until just combined.
Cover the dough with plastic wrap and refrigerate it for at least 20 minutes.
In a small bowl combine the sugar and cinnamon. Using a spoon or cookie scoop, roll the dough into small balls until they are round and smooth. Drop and roll the balls into the cinnamon-sugar mixture and coat well till they are completely covered.
Place them on a baking sheet, lined with parchment paper. Bake for about 9 minutes until the edges are set and golden. The cookies may look under-baked at first, but they are done!
Remove the snickerdoodles from the oven and allow them to sit on the pan for 5-10 minutes before moving to a cooling rack.