Whisk the flour, baking powder, and salt together in a medium bowl. Set aside.

In a large bowl using a handheld or a stand mixer fitted with a paddle attachment, beat the butter and sugar together on high speed until completely smooth and creamy, about 2 minutes. Add the egg and vanilla and beat on high speed until combined, about 1 minute. Scrape down the sides and up the bottom of the bowl and beat again as needed to combine.

Add the dry ingredients to the wet ingredients and mix on low until combined. Dough will be a bit soft. If the dough seems too soft and sticky for rolling, add 1 more Tablespoon of flour.

Divide the dough into 2 equal parts. Roll each portion out in a rectangle (about 9×7 inches) onto a floured silicone baking mat (or floured parchment paper) to about ¼" thickness. Spread 1 Tablespoon of melted butter onto each rectangle. Mix the granulated sugar and cinnamon together then sprinkle evenly over each.

Working slowly, tightly roll up each rectangle into a 9-inch log. If the dough is cracking at all, use your fingers to smooth it out. Some cracks are OK. Chill the logs of dough for at least 2 hours (or freeze up to 3 months).

Preheat oven to 350°F (177°C). Line a large baking sheet with parchment paper or a silicone baking mat.

Remove dough logs from the refrigerator. Cut into ½ inch slices. Place slices onto baking sheets about 2 inches apart.

Bake for 10-11 minutes, until lightly browned on the sides. Remove from the oven, allow to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely before icing.

Whisk all of the icing ingredients together. Drizzle over cookies.

Cover and store cookies at room temperature for up to 5 days.