Preheat oven to 350 degrees. Line cookie sheets with silpat liner or parchment paper. Set aside.
Unwrap candy and place into a bowl. Set bowl in the fridge while you prepare the dough.
In the bowl of a stand mixer, or in a mixing bowl with a hand blender, combine butter and sugar. Beat together until combined and fluffy (about 2 minutes). Add egg and vanilla extract. Blend until combined.
In separate bowl, combine flour, baking powder, and salt. Stir with a whisk to break up any clumps.
Add flour mixture into butter mix, 1 cup at a time, mixing well after each addition. The dough will be thick & crumbly but should hold together when formed into a ball.
Combine additional sugar and cinnamon in small bowl.
Using a small cookie scoop, or about 2 tablespoons of dough, scoop dough and stuff a caramel apple milky way inside. Form a ball around the candy, making sure to completely cover it. Roll the ball in the cinnamon/sugar mix and place on cookie sheet.
Bake for 11-14 minutes. I found 12 minutes to be the perfect time. Cookies will be puffy, won't spread much, and the edges will be a light golden brown.
Let cool on cookie sheet for 2 minutes before removing to a cooling rack to cool completely.
These are best served warm but still yummy at room temperature. We have also warmed up leftovers in the microwave for a few seconds for a warm, melty treat.