Preheat oven to 350F (177C)
Place butter in a large bowl and using an electric beater or stand mixer beat until creamy and smooth.
Add sugar and beat until light and fluffy.
Add lightly beaten egg yolk. Scrape down sides of bowl as needed to evenly incorporate all ingredients and stir in vanilla extract.
In a separate bowl, combine flour, cocoa powder, and salt.
Gradually add flour mixture to the butter mix. Make sure to scrape the sides and bottom of the bowl with a spatula frequently--this is a dry mix and you want to make sure you don't leave residual dry mix at the bottom of the bowl.
Roll dough into 1 ½" balls. Place balls on parchment paper lined cookie sheet and press down with your thumb in each, creating a (flatter) thumbprint cookie. Place on wax-paper lined plate.
Place cookies in freezer for 10-15 minutes before baking to help them keep their shape.
Once cookie dough has chilled, bake on 350F (177C) for 10-11 minutes
Immediately upon removing cookies from the oven, re-indent the thumbprints using the rounded back of a teaspoon (do not use your thumb as the cookies will be too hot).
Allow cookies to cool completely on pan before filling with peanut butter filling.
Combine peanut butter, white chocolate chips, and butter in a medium-sized microwave-safe bowl.
Microwave on 15-second increments, stirring in-between, until chocolate chips are melted and ingredients are well-combined and smooth.
Stir in vanilla extract.
Immediately spoon fudge mix into the craters of the cooled cookies.
Drizzle with melted chocolate, if desired.