In the bowl of a stand mixer or using a hand-held mixer, beat the vegan butter until peaks form.
Add white sugar, vanilla extract, salt, and dairy-free milk, mix until creamy.
Add flour and mix until you have a smooth dough.
Form the dough into a ball, wrap with plastic wrap, and refrigerate for 30 minutes.
Form dough into two squares, place each on a plastic wrap, and roll them out into a thin rectangle.
Spread rectangles with melted vegan butter. Mix brown sugar and cinnamon, then sprinkle over the vegan butter.
Roll the rectangles into a long log (use the plastic wrap as help). Wrap the log in plastic wrap and refrigerate for one hour.
Preheat your oven to 390°F (200°C).
Slice into ¼-inch (1cm) thick cookies and place on a with parchment paper lined baking sheet.
Bake the cookies for 10 minutes in the preheated oven.
Allow cookies to cool for 5 minutes on the baking sheet, then transfer to a cooling rack to cool completely.