In a large mixing bowl, cream together the softened butter and 1 cup of granulated sugar for about 4 minutes, until the mixture is light and fluffy. Add the egg and vanilla extract, and continue mixing for another minute until fully incorporated. Gradually stir in the all-purpose flour, baking soda, and salt, mixing until a dough forms. Chill the dough in the refrigerator for 10-15 minutes to make it easier to handle.
While the dough is chilling, combine 1/2 cup granulated sugar with 2 teaspoons ground cinnamon in a shallow bowl to create the cinnamon-sugar coating. Once the dough has chilled, roll it into 16 to 24 balls, depending on your desired cookie size. Drop each dough ball into the cinnamon-sugar mixture and coat well before placing them onto a parchment- or Silpat-lined baking sheet.
Bake the coated cookie dough balls in a preheated 350°F (175°C) oven for 9 to 11 minutes, or until the edges are lightly golden brown but the centers are still soft. When the cookies come out of the oven, you may sprinkle them with any remaining cinnamon-sugar mixture for extra flavor. I almost always add this sprinkle as it gives the tops a lovely finish.
While the cookies cool, melt 1 tablespoon of butter in a small saucepan over low heat. Once melted, remove the pan from the heat and immediately stir in the can of dulce de leche until smooth and well incorporated. The touch of butter really adds silkiness to the filling.
Once the cookies are completely cool, spread a layer of the dulce de leche filling on the bottom of one cookie, then top with another cookie to create a sandwich. Repeat for the remaining cookies. For a special touch, I like to let the assembled sandwich cookies rest for an hour so the filling sets up and the flavors meld together.