PREHEAT oven to 350° F.
FOR MORSEL-PEANUT BUTTER FILLING:
COMBINE semi-sweet and butterscotch morsels in medium bowl. Stir in 1/2 cup peanut butter until well combined.
BEAT butter and remaining peanut butter in large mixer bowl on medium speed for 30 seconds. Add granulated sugar, brown sugar, baking soda and salt; beat until combined. Add eggs, vanilla extract and milk; beat until combined. Beat in as much flour as possible. Stir.
SHAPE 1 tablespoon of dough into ball; flatten into 2-inch diameter circle. Place 1 teaspoon of Morsel-Peanut Butter filling in center of circle. Fold dough around filling, forming a ball. Place balls 1-inch apart on ungreased baking sheets.
BAKE for 10 to 12 minutes or until golden brown. Cool on baking sheets for 1 minute; remove to wire racks to cool completely. Drizzle melted white morsels over cooled cookies. Store in airtight container at room temperature up to 3 days.
NOTE: May freeze for longer storage.