In a large bowl, beat the butter and sugar until smooth and fluffy, about 2 minutes. Add the egg and vanilla and mix again to combine.
Sift the flour and baking soda over the wet mixture and beat until combined. Use your hands to form the dough into a rough rectangle shape and then wrap the dough in plastic wrap. Place it in the fridge for 30 minutes to chill and set.
Once the dough has cooled, roll out the dough. Lightly sprinkle some flour over a clean, flat work surface. Use a rolling pin to roll out the dough into a large rectangle that is 1/2 cm thick. Rotate the sheet of dough often so that it doesn't stick to the counter.
In a small bowl, combine the remaining sugar and cinnamon. This will be the filling for the cinnamon roll cookies.
Next, use a pastry brush to spread the milk evenly across the rectangular dough. The milk will make the dough moist, which will allow the filling mixture to stick. Sprinkle the filling mixture evenly across the dough and gently use your hands to pat it down into the dough.
Next we will roll the cookies into a log. Being by rolling the cookies from the longest edge of the dough. Roll the dough fairly tight so that the filling does not fall out. Continue to roll the dough all the way to the other edge of the dough.
Once rolled, place the log dough, seam side down onto a sheet of plastic wrap and wrap the dough tightly. Place the log of dough in the fridge for 15 minutes to set.
Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper and set aside.
Unwrap the dough from the plastic wrap. Use a serrated knife to slice the dough into rounds that are 1/2 cm thick. Place the cookies on the baking tray about an inch apart. Bake the cookies in the center of the oven for 8-10 minutes, or until the bottoms are golden brown.
Remove the cookies from the baking tray and transfer them to a cooling rack to cool off before eating! Enjoy!