Preheat oven to 350F.
In a small bowl, stir together the flour, baking soda, baking powder and salt. Set aside.
In a large bowl, beat together the butter and peanut butter thoroughly.
Add the sugars and beat for 2 minutes, until creamy and light.
Add the egg and vanilla extract, beat for 30 seconds, then slowly incorporate the flour mixture until just incorporated.
Use a cookie scoop to portion out the dough on a lined cookie sheet.
Use a fork to press down on the cookies, flattening them and making a classic criss-cross pattern.
Bake cookies for 8-10 minutes until lightly golden and set.
Cool on the cookie sheet for about 30 minutes.
Melt candy melts in a microwave-safe bowl for 25 seconds. Stir and reheat as needed.
Dip each cookie individually in the melted candy melts, covering up to one half of each cookie.
Place cookie back on the cookie sheets and decorate with Christmas sprinkles as desired.
Allow candy melts to set before storing or serving.