Preheat oven to 350 degrees F. In a large mixing bowl, beat together butter, shortening, and sugars. Add eggs one at a time, mixing well after each addition. Mix in vanilla extract. Add flour, baking soda, and salt and mix just until blended. Stir in oats, chocolate chips, and marshmallows.
Line a baking sheet with a silicone mat. Drop cookies by spoonfuls on baking mat, about 2 inches apart. Bake at 350 degrees F for 11 to 13 minutes. Let cool on pan a few minutes before transferring to wire racks to cool completely. Store in an airtight container.