Preheat the oven to 400 degrees. You will need an ungreased, non-stick baking sheet for these cookies. In the bowl of a stand mixer or a large bowl, beat together butter and sugar until it is fluffy.
Add the egg and vanilla and mix until fully combined. Add flour and salt and beat until the mixture is uniform.
Scoop the dough into the cookie press fitted with the desired disk shape. Holding the press vertical to the pan, press out each cookie, lifting straight up after pumping the handle.
Bake for 7-8 minutes or until the cookies just begin to turn golden around the edges. Remove from the pan and let cool completely.
For Filling: Beat together dulce de leche and dark rum until completely smooth.
To assemble: Scoop the mixture into a zip-top bag and snip one tip. Pipe the dulce de leche onto one side of each cookie. Top with a slice of fresh banana. Then place another cookie on top to completely sandwich the filling.