Heat oven to 350°F. Cut peanut butter cookie dough into 36 equal pieces; roll each into ball. On ungreased cookie sheets, place balls 2 inches apart. With fork dipped in sugar, flatten each ball slightly in crisscross pattern.
Bake 8 to 11 minutes or until light golden brown. Immediately remove from cookie sheets. Repeat with chocolate chip cookie dough.
In small bowl, mix frosting and peanut butter until well blended. Spread about 1 tablespoon frosting mixture on bottom of each peanut butter cookie. Top each with chocolate chip cookie, bottom side down; press gently. Store in refrigerator.