Prepare the Cookie Dough: Begin by sifting the flour and salt together in a large mixing bowl. Stir in the chopped walnuts until they are evenly distributed throughout the dry ingredients, then set this mixture aside.

Cream Butter and Sugar: In a stand mixer, combine softened unsalted butter and powdered sugar, beating them together until light and fluffy. Add in the vanilla extract, mixing it well into the creamed mixture for added flavor.

Combine Ingredients: Gradually add the flour-walnut mixture to the butter-sugar mix while reducing the mixer speed to low. Beat until just incorporated; avoid overmixing as it can lead to dense cookies.

Chill Dough and Bake Cookies: Gather your dough into a disc shape, wrap it in plastic wrap, and refrigerate for about 30 minutes until chilled. Preheat your oven to 350°F (175°C) and line two baking trays with parchment paper before rolling out chilled dough on a lightly floured surface.

Prepare Ice Cream Mixture: In a medium saucepan, combine milk, heavy cream, salt, and dulce de leche over medium heat. Bring this mixture to a simmer until all components are well dissolved, then strain it into another bowl for cooling before churning in an ice cream maker.

Assemble Sandwiches: Once your cookies have cooled completely and your ice cream has firmed up in the freezer, use a cookie cutter to cut out discs of ice cream. Layer one disc between two cookies and gently press them together before optionally rolling or sprinkling with chopped walnuts on the edges for an extra crunch.