Melt butter in a Dutch oven over medium heat. Remove from heat, and stir in oats and next 7 ingredients.
Drop oat mixture by tablespoonfuls 3 inches apart onto a parchment paper-lined baking sheet. Spread each dollop of cookie batter to form a 3-inch circle.
Bake at 350° for 9 to 11 minutes or until edges are golden. Remove from pan, and cool completely on a wire rack.
Swirl peanut butter into softened ice cream. Freeze 30 minutes. Scoop ice cream evenly on flat sides of half of cookies; top with remaining cookies, flat sides down. Roll sides of sandwiches in coarsely chopped peanuts. Place in plastic or wax paper sandwich bags, and freeze at least 1 hour.
Note: Do not substitute a greased baking sheet for parchment paper. Cookies will slide and tear.