Place the butter and granulated sugar into a large bowl. Using a hand mixer, cream together the butter and sugar on medium speed for 1 minute, or until combined.

Add the egg and vanilla extract and continue to beat until light and fluffy, 30 seconds to one minute.

Turn the mixer to low and add the flour, baking soda, and salt to the bowl. Beat the mixture until all ingredients are combined, about 1 minute.

Lay a sheet of plastic wrap on the counter and turn the cookie dough onto it. Flatten into a round disc and cover completely with plastic wrap. Refrigerate the cookie dough for 30 minutes.

While the cookie dough chills, prepare the cinnamon sugar filling. In a medium bowl, whisk together the brown sugar, cinnamon, salt, and melted butter until thoroughly combined. Set aside.

Remove the chilled cookie dough from the refrigerator. Generously dust a clean work surface with flour.

Unwrap the cookie dough and place on the work surface. Using a rolling pin, roll the dough into a rectangle approximately 14x9 inches, and 1/4-inch thickness.

Spread an even layer of cinnamon sugar filling over the rectangle of cookie dough.

Working gently, tightly roll the cookie dough lengthwise, into a 14 inch log. Cover the log with plastic wrap, and refrigerate for 1 hour.

Line two baking sheets with silicone baking mats or parchment paper. Set aside.

Preheat the oven to 350°F.

Remove the log of cookie dough from the refrigerator. Using a very sharp knife, slice the log into 1/2-inch thick cookies. Place the slices onto the baking sheets roughly 1 1/2 inches apart.

Bake the cookies until the bottom edges are lightly browned, 11-12 minutes.

Check to see that cookies are done. Remove from oven or add time as needed.

Allow the cookies to cool for 5 minutes on the baking sheets, then transfer them to cooling racks to cool completely before icing.

To make the glaze, place the powdered sugar and salt in a medium bowl.

Add the vanilla and milk. Whisk slowly to combine. If the icing is too thick, add another 1/2 to 1 tsp. of milk.

Use a spoon to drizzle thin strands of icing across each cookie. Allow to set for 10-15 minutes before serving.