How to Make It
Preheat oven to 350°. Whisk together first 4 ingredients in a medium bowl. Beat 1/2 cup butter at medium-high speed with an electric mixer until fluffy. Add brown sugar and 3/4 cup powdered sugar; beat until well blended. Beat in 3/4 cup peanut butter, scraping down sides as needed. Add eggs, 1 at a time, beating until blended after each addition. Beat in vanilla. Reduce speed to medium-low, and gradually add flour mixture, beating just until blended.
Shape dough into 30 balls. Place 12 balls 2 inches apart on a parchment paper-lined baking sheet. Press thumb into each ball, forming an indentation.
Bake at 350° for 12 minutes or until set; cool 5 minutes. Transfer cookies to a wire rack, and cool 15 minutes. Repeat with remaining dough.
Beat 1/4 cup peanut butter and 2 Tbsp. butter at medium speed until smooth. Microwave chopped chocolate in a microwave-safe bowl at HIGH 1 to 2 minutes or until smooth, stirring every 30 seconds. Add melted chocolate to peanut butter mixture, and beat at medium speed just until blended. Gradually add 1 1/2 cups powdered sugar to peanut butter mixture alternately with 2 Tbsp. milk, beginning with sugar. Beat at low speed just until blended after each addition. Beat in up to 1 Tbsp. milk, 1 tsp. at a time, until desired consistency is reached.
Spoon filling into a zip-top plastic bag; snip 1 corner of bag to make a small hole, and pipe filling into indentations in cookies.