Put the butter and 1/2 cup sugar in the bowl of a stand mixer fitted with the paddle attachment. Cream until smooth.
Add egg and vanilla. Mix until combined.
Slowly mix in AP flour, cream of tartar, salt, and baking soda until well combined. The dough will feel sticky.
Chill for best results. I recommend pre-shaping the cookie dough into 12 individual balls and placing them in the fridge for 1-2 hours, or in the freezer for 20 minutes if pressed for time.
Once the cookie dough is thoroughly chilled, start with one ball by taking it out of the fridge and placing it on a piece of plastic wrap. Place a sheet of parchment paper over the top of the ball. Using a rolling pin, roll the dough into a flat disk, then peel off the parchment.
Place a melon pan bread ball on top of the cookie dough disk, then gently lift the plastic wrap underneath, using it to adhere the cookie dough to the bread dough as best as possible.
Peel off the plastic wrap. Roll the melon pan ball (cookie side facing down) into your cinnamon sugar mixture generously, before scoring lines into the top of the ball. A plastic bench scraper or the back of a knife will work great.
Place on a tray and repeat until you have all 12 melon pan.
Cover the tray with plastic wrap and let proof again until big and puffy, but not doubled in size. (About 45 mins)
Remove the plastic wrap and place in a preheated oven at 350f for 12-15 minutes until lightly golden. the time will depend on how large you've made your melon pan. To check for doneness, tap the top of the shell with your fingernail. It should feel hard and have a slight hollow sound.
Let cool and enjoy!