Heat oven to 350 degrees.
In larger bowl, beat butter, brown sugar, and peanut butter until well blended.
Add egg and vanilla, beat well.
Stir together flour, baking powder, baking soda, and salt.
Gradually add flour mixture to peanut butter mixture, beat until well blended.
Shape dough into 1-1/4 inch balls, roll balls in granulated sugar. Place on ungreased cookie sheet.
With the tines of a fork, flatten ball. Flatten again in opposite direction, forming crisscross marks.
Bake 9 to 10 minutes until light brown and cookie is set.
Cool slightly, Remove from cookie sheet to wire rack. Sandwich Reese's Peanut Butter Cup between two peanut butter cookies. Let cool completely.