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

In a large bowl, beat the butter and sugar together on high speed until smooth and creamy, about 2 minutes. Add the egg and vanilla and beat until combined, about 1 minute. Scrape down the sides and beat as needed.

Add the dry ingredients to the wet ingredients and mix on low until combined. If the dough is too soft, add 1 more tablespoon of flour.

Divide the dough into 2 equal parts. Roll each into a rectangle about 9x7 inches and ¼-inch thick. Spread 1 tablespoon of melted butter onto each rectangle.

Mix the sugar and cinnamon together and sprinkle over each rectangle. Roll each up into a 9-inch log. Chill for at least 2 hours.

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

Cut the chilled logs into ½ inch slices and place on baking sheets about 2 inches apart.

Bake for 10-11 minutes until lightly browned. Allow to cool on the baking sheet for 5 minutes before transferring to a wire rack.

Whisk all icing ingredients together and drizzle over cookies.