Preheat oven to 350°F. Line baking sheets with parchment paper and set aside.
In a large bowl, beat butter, peanut butter, brown sugar, and granulated sugar until creamy and smooth, about 2-3 minutes.
Add eggs and vanilla. Mix well, stopping to scrape the bottom and sides of the bowl.
Add the flour, cornstarch, baking powder, baking soda, and salt. Mix just until combined.
Use a large cookie scoop to scoop out large balls of cookie dough. Shape each ball of dough into a sort of puck shape about 1-inch thick, spacing them apart on the prepared baking sheets. You should get about 18-20 cookies.
Chill the cookies in the freezer for 15 minutes, then bake for 12–13 minutes until set around the edges. Let cool for 10 minutes on the baking sheet, then transfer to a wire cooling rack.
Carefully melt the chocolate chips in the microwave in a microwave-safe bowl using short 20-second bursts of heat, stirring between each burst until melted. Spoon about 1 tablespoon of melted chocolate on top of each cookie and spread it around to form a chocolate coating. Sprinkle the top of each cookie with some of the muddy buddies pieces while the chocolate is still melted so they stick.
Let the cookies sit at room temperature until the chocolate firms up before dusting lightly with a little powdered sugar.