Preheat the oven to 350°F. Lightly grease two baking sheets, or line with parchment paper.
1. For the cookies: In a large bowl, cream together the butter, sugars, and salt until light and fluffy. Add the vanilla, and then the bananas.
2. The mixture will look curdled; that's OK. Beat in the eggs, one at a time.
3. Whisk together the flour and baking soda; add to the banana mixture, mixing until evenly combined. Scrape the bottom and sides of the bowl, then mix for 1 minute more.
4. Stir in the chips and walnuts.
5. Scoop the dough by the quarter cup for large cookies, and by the tablespoon for small cookies. Allow plenty of space between them.
6. Bake for 12 to 14 minutes, until the tops spring back when lightly touched with your finger, and the edges are a very light golden brown. Remove from the oven and cool on the baking sheet for 10 minutes before transferring the cookies to a rack to finish cooling completely before filling.
7. For the filling: Beat together the cream cheese, confectioners' sugar, and vanilla until smooth. Add just enough milk to make the mixture a spreadable consistency. Stir in the walnuts.
8. To assemble: Spread the bottom of one of the cookies with 2 tablespoons of the filling. Place another cookie on top of the filling, bottom side down.