Mix the ingredients together for the cinnamon sugar in a small bowl and set aside.
Remove the dough from the fridge and place it on a lightly floured surface. Roll out the dough into an 10" x 10" square. You can square out the corners with your hands first before and after rolling the dough to keep the corners from rounding too much.
Remove the butter block from the freezer, unwrap it, and place it in a diamond position on top of and in the center of the dough.
One corner at a time, fold the corners of the dough in towards the center of the butter block. The dough corners may slightly overlap. Pinch along the seams to seal the butter block into the dough.
In our experience, since vegan butter is typically not as firm as non-vegan butters the butter might start becoming soft. If that is the case, wrap the dough in plastic wrap and place it in the freezer for 10 minutes to give the butter time to firm up before continuing.
Flip the dough so it is seam-side down. Lightly flour the top and bottom of the dough. Use a rolling pin to gently press down along the length of the top of the dough to create little indents in the dough. Turn the dough 90º and gently press down along the length of the dough again. The goal here is to make the butter inside the dough a little more pliable so it is easier to roll.
Roll out the dough into a rectangle that is roughly three times longer than it is wide, dusting more flour as needed and occasionally moving the dough to ensure it doesn't stick to the surface. Make sure to roll both towards you and away from you to ensure the butter is evenly distributed inside the dough. Roll until the dough is between ¼ inch and ½ inch thick.
Fold the dough into thirds like a letter by lifting one end (a third of the dough) of the rectangle up onto the center of the dough, followed by the other end of the rectangle. The resulting dough will be three layers stacked on top of each other. This is your first "turn" of the dough.
Place the dough in the fridge and allow it to rest for 30 minutes.
Remove the dough from the fridge. Repeat the rolling and folding process, except spread a layer of the cinnamon sugar over the surface of the dough before folding it. This is your second "turn". Wrap and chill again, if necessary.
Rotate the dough 90º a final time. Repeat the rolling process and spread one more layer of cinnamon sugar again before doing the same fold as before. This is your third and final "turn".
Wrap the dough in plastic wrap and place it in the fridge. Let it rest for 30 minutes.