Whisk flour, oats, baking soda and salt in medium bowl.
Beat butter and brown sugar in large bowl at medium speed 3 minutes or until light and fluffy. Beat in peanut butter and vanilla. Add eggs one at a time, beating just until combined. At low speed, beat in flour mixture just until combined.
Stir in peanuts, peanut butter chips and toffee bits. Cover and refrigerate 2 to 3 hours or overnight.
Preheat oven to 375 degrees F. Line cookie sheet with parchment paper. Gently form into balls and flatten slightly to about ½- to ¾- inch thickness. Freeze dough on baking sheets for 10 minutes or until firm. Bake about 12 minutes or until light brown on edges. Cool on baking sheet on wire rack 3 minutes. Place cookies on rack to cool completely before storing.