Preheat oven to 350 degrees F.
Place parchment paper on 2 or 3 large baking sheets. In a medium mixing bowl, mix together flour, baking soda, and salt. Set aside. With an electric mixer, cream butter, peanut butter, brown sugar, and 1 cup of sugar until creamy. Add eggs, one at a time, beating well after each addition.
Gradually add dry mixture to wet mixture.
Pour remaining 1/4 cup sugar onto a plate or small pour.
Roll dough into tablespoon sized balls and then roll in sugar. Place on baking sheet, approximately 2 inches apart.
Press 1/2 tsp. Sized indent into center of cookies.
Make filling by beating peanut butter and cream cheese until smooth.
Beat in sugar, egg yolk, and vanilla. Spoon approximately a teaspoon of filling into indent of cookies.
Bake 10-12 minutes, until slightly golden brown on edges. Allow to cool 5 minutes before moving to cooling rack.
Once cookies have almost completely cooled, make drizzle topping.
In a small saucepan, melt butter.
Remove from heat and whisk in powdered sugar and cocoa.
Add water, a tablespoon at a time, until desired consistency is reached.
Whisk in vanilla.
Drizzle over cookies and leave to set.