For the cookies: Preheat your oven to 350° F. Line 2 baking sheets with parchment paper; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, peanut butter, 1 cup of the granulated sugar, and the brown sugar together until creamy and smooth, about 1 minute. Add in the eggs, one at a time, mixing well after each addition, followed by the vanilla extract. Lastly, add in the baking powder, baking soda, and flour and mix until a soft dough comes together. Meanwhile, add the remaining 1/3 cup granulated sugar to a separate small bowl and set aside.
Using a 2-Tablespoon size cookie dough scoop, portion out 2 Tablespoon-size balls of cookie dough and roll them into a ball. Roll the ball into the granulated sugar and place 1-2" apart on the baking sheets.
Bake for 8-10 minutes, rotating pans halfway through baking time to ensure even cooking. Cool for about 10-15 minutes on the pans before carefully transferring to wire racks to cool. Cookies will be very delicate. Cool completely.
For the ganache: In a medium microwaveable bowl, add the chocolate chips and peanut butter. Microwave on HIGH power for 30 seconds. Stir. Microwave on HIGH power for another 30 seconds, stirring until melted and smooth. Drop a heaping teaspoon or two of the melted ganache on top of each cookie and spread it out. Garnish with the muddy buddies while the ganache is still tacky. Allow the ganache to set, about 20 minutes, before serving or storing.