Trace a 9x16-inch rectangle on a sheet of parchment or wax paper.

Combine granulated sugar and 2 tablespoons cinnamon in a small bowl. Set aside.

Whisk together flour, baking powder, 1 teaspoon cinnamon, and salt in a bowl; set aside.

Cream butter and brown sugar in the bowl of a stand mixer fitted with the paddle attachment on medium speed until smooth. Scrape bowl with rubber spatula.

Add eggs (one at a time) and vanilla; mix on low speed until incorporated. Scrape bowl again.

With mixer on low speed, add dry ingredients, blending just to incorporate; do not overmix.

Pat dough into a rectangle using your hands. (Turn parchment over so you don't get ink on your dough.) Have your bowl of ice water ready for dipping your hands. (see notes)

Sprinkle half the cinnamon-sugar mixture over dough. (about 1/4 cup)

Roll dough tightly into a log, beginning on a long side and using the paper to help you.

Dust outside of log with remaining cinnamon-sugar mixture. (I didn't use all of it.) Wrap log in plastic and let chill at least 4 hours. (I prefer to do it overnight.)

Position the rack in the centre of the oven and preheat to 350 degrees F. Line two baking sheets with parchment paper.

Slice chilled dough with an electric carving knife or sharp serrated knife into 1/2-inch-thick slices and arrange on prepared baking sheets, spacing 1 inch apart, 18 - 20 per baking sheet. Trim the edges first if you want all the slices to be perfect… but I think you need at least two "tasters!"

Bake one tray at a time until golden, 10 - 13 minutes, rotating sheet after 7 - 8 minutes. (See notes) Let cool on pan 5 minutes, then transfer parchment with cookies to a baking rack.

To Ice: Sift powdered sugar into a medium bowl; add egg whites or meringue powder. Whisk in 2 tablespoons of warm water (I used my hot water tap), adding more water if necessary until you get a nice thick consistency. Pour into a quart freezer ziplock bag, twisting the top of the bag to hold. Cut a tiny hole on the end and drizzle over cooled cookies; let stand until icing dries. (I had to transfer the cookies to a wire rack using an offset spatula after a half hour so that the icing would dry completely before stacking and freezing them.)