Make the swirl. Melt the butter, then stir in the remaining ingredients. Set aside.
Make the cookie dough. Beat the butter and both sugars together until light and fluffy. Beat in the egg and vanilla until fully incorporated- roughly 1-2 minutes.
Mix in the flour, salt, and baking soda and mix until just incorporated. Roll out dough so it is a rectangle about 8 x 14 inches. Trim the edges so they are straight and even.
Carefully spread the cinnamon swirl mixture over the dough. Leave a border on both short sides and one longer side.
Roll the cookie dough into a log, starting with the longer side that doesn’t have a border. Make sure you roll the log tightly.
Wrap the cookie dough and chill for about 20 minutes in the freezer. You can bake without chilling, but I find chilling makes it easier to cut even rounds.
Preheat the oven to 350°F as the dough chills. Line two baking sheets with parchment paper.
Slice the cookies roughly 1/4-inch thick. Place cookies on the baking sheets about 2 inches apart.
Bake for 8-9 minutes, or until the edges are a light golden brown.
Remove and allow to rest on the baking sheets for a minute before transferring to a wire rack to cool completely.
While the cookies are cooling, make the glaze.
Mix together the cream cheese, butter, and vanilla until they are smooth. Add in the powdered sugar one cup at a time, mixing it thoroughly before adding the next cup. It will get crumbly and this is normal.
Add the heavy cream one tablespoon at a time, mixing well as you do so.