Preheat oven to 350 degrees F. Grease a cookie sheet; set aside. In a small bowl combine flour, baking soda, the 1/2 teaspoon salt, and the baking powder; set aside. In a large bowl combine butter and peanut butter. Beat with an electric mixer on medium speed until combined. Beat in granulated sugar and brown sugar until fluffy. Beat in egg and vanilla just until combined. Stir in flour mixture and oats just until combined.
Drop dough by rounded teaspoons 2 inches apart onto prepared cookie sheet. Bake for 8 to 10 minutes or until edges are light brown and centers are set. Cool on cookie sheet for 1 minute. Transfer cookies to a wire rack; let cool.
Meanwhile, in a medium bowl combine the hot water and the 1/4 teaspoon salt. Stir until salt dissolves. Add marshmallow creme, shortening, and powdered sugar. Beat with an electric mixer on medium speed until combined.
Spread marshmallow mixture on the flat side of half of the cookies. Top each frosted cookie with another cookie, flat side down.