Prepare the cookie dough by sifting together flour and salt, then mixing in the chopped walnuts.
Cream together softened unsalted butter and powdered sugar until light and fluffy, then incorporate vanilla extract.
Combine the flour-walnut mixture into the butter mixture until just incorporated, then refrigerate the dough for about 30 minutes.
Preheat oven to 350°F (175°C), roll out chilled dough, cut into rounds, and refrigerate again before baking until lightly browned.
Combine milk, heavy cream, salt, and dulce de leche in a saucepan, heat until simmering, then cool and process in an ice cream maker.
Assemble sandwiches by placing ice cream discs between cookies and rolling the sides in chopped walnuts.