Beat butter at medium speed with an electric mixer until creamy. Gradually add sugars, beating until smooth. Add peanut butter and vanilla, beating until blended. Add eggs, 1 at a time, beating after each addition.
Combine flour, baking soda, and salt; gradually add to butter mixture, beating at low speed just until blended. Stir in granola and morsels; cover and chill 2 hours.
Shape dough into 1 1/2-inch balls, and place the balls 2 inches apart on baking sheets.
Bake at 375° for 8 to 10 minutes or until golden. Cool on baking sheets 5 minutes. Remove to wire racks to cool completely.
Note: For larger cookies, drop by 1/4 cupfuls onto baking sheets. Bake at 375° for 18 to 20 minutes.