Start by creaming the softened butter with granulated and brown sugar until light and fluffy. Add eggs and vanilla, mixing until fully combined. Gradually fold in flour, crushed graham crackers, baking soda, baking powder, and salt, mixing just until incorporated.
Divide dough into twelve 1/2 cup portions for large cookies. Roll each into a ball and place six per cookie sheet. Flatten slightly and bake at 350°F (175°C) for 12–15 minutes until golden. Let them cool on the pan for 20 minutes before frosting.
Whip the cream cheese until smooth, then gradually blend in marshmallow creme. Add powdered sugar in batches until creamy and fluffy. Transfer frosting into a piping bag and pipe a spiral onto each cooled cookie.
Pipe caramel in a zig-zag pattern over the frosted cookies and sprinkle coarse sea salt on top. Serve immediately or chill for a firmer texture.