Preheat oven to 350°. In a medium bowl with a hand or stand mixer on medium speed, cream butter and sugars until smooth. Add peanut butter and mix until combined; then add eggs and vanilla, scraping down sides of bowl as needed.
In another medium bowl, whisk together oats, flour, and baking soda. Add to butter mixture and mix on low until well incorporated. Stir in chocolate chips with a wooden spoon.
Drop dough by rounded tablespoons 1 inches apart onto ungreased baking sheets. (I used a cookie scoop and found I needed to use a fork to press the tops of the cookies down a bit as they do not spread out much) Bake 10 to 12 minutes (In my oven 14 minutes), switching position of pans halfway through baking, or until lightly browned but still soft in the center. Transfer cookies to racks to cool. (I found it helped to leave cookies on the sheet for a minute before removing them to racks to cool).
The Twist: Ice Cream Sandwiches. Turn these great cookies into superb ice cream sandwiches: Soften the ice cream of your choice, 10 minutes. Spread 1/4 cup onto flat side of 1 cookie and top with another cookie, flat side down, pressing lightly. Chill sandwiches in freezer about 10 minutes, just long enough to chill ice cream but not enough to harden cookies. Eat immediately.