Mix oats, flour, graham cracker crumbs, baking soda, baking powder, cinnamon, and salt together in a bowl.
Beat butter with an electric mixer in a large bowl for 30 seconds. Mix in brown sugar, white sugar, milk, eggs, and vanilla until well blended. Mix in flour mixture until combined. Chill in the refrigerator for 1 to 2 hours.
Preheat the oven to 350 degrees F (175 degrees C). Slice 13 to 15 marshmallows into thirds. Unwrap 36 to 45 candy kisses. Set remaining marshmallows and candy kisses aside for another use.
Drop rounded balls of dough onto an ungreased baking sheet.
Bake in the preheated oven for 8 minutes. Remove cookies from the oven and immediately use the back of a spoon to make an indentation in the center of each cookie. Place a marshmallow slice in the indentation and return to the oven until marshmallow is slightly melted, about 1 minute.
Remove from the oven and push the point of a candy kiss down into each marshmallow. Return to the oven for 1 more minute.
Cool on the baking sheet for briefly before removing to a wire rack to cool completely.