I whisk the flour, baking powder, and salt together first so they're evenly distributed. In a separate bowl, I beat the softened butter and sugar until it's pale and creamy, then mix in the egg and vanilla. Once that's smooth, I add the dry ingredients and mix just until a soft dough forms.
I divide the dough in half and roll each portion into a rectangle about 9 by 7 inches on a lightly floured mat. I try to keep the thickness even, around a quarter inch, so the swirl bakes uniformly. Working on a silicone mat instead of a floured counter makes the whole process a lot less messy.
I brush each rectangle with melted butter, then sprinkle the cinnamon sugar mixture evenly over the top. I make sure to spread it all the way to the edges so every slice gets that cinnamon roll flavor in every bite, not just the center.
Starting from one long edge, I roll each rectangle up tightly into a log. If the dough cracks a little, I just smooth it out gently with my fingers. Rolling slowly keeps the swirl tight instead of loose and uneven.
This is the step I never skip. I wrap the logs and refrigerate them for at least two hours so the dough firms up. Chilling keeps the cookies from spreading out and losing their pretty spiral shape in the oven.
Once chilled, I slice each log into rounds about half an inch thick and space them two inches apart on a lined baking sheet. They bake at 350°F for about 10 to 11 minutes, just until the edges turn lightly golden.
I let the cookies rest on the baking sheet for five minutes before moving them to a wire rack to cool completely. Icing warm cookies makes the icing melt and slide right off, so I always wait until they're fully cool before drizzling.