Preheat the oven to 350°F (175°C) and place a rack in the middle position.
In a medium bowl, cream together the 1/2 cup butter, 1/2 cup white sugar, and 1/3 cup packed brown sugar until smooth (butter should be softened).
Stir the 1/2 cup peanut butter, 1/2 teaspoon vanilla extract, and 1 egg into the creamed mixture until well blended.
In a separate bowl, combine 1 cup all-purpose flour, 1 teaspoon baking soda, and 1/4 teaspoon salt.
Stir the dry ingredients into the wet mixture just until moistened; do not overmix.
Mix in 1/2 cup rolled oats and 1 cup peanut butter and chocolate swirl chips until evenly distributed.
Drop the dough by tablespoonfuls onto lightly greased cookie sheets, spacing the cookies about 2 inches apart.
Bake for 10 to 12 minutes in the preheated oven, or until the edges start to brown.
Cool the cookies on the cookie sheets for about 5 minutes, then transfer them to wire racks to cool completely.