2Tablespoons(15 g) unsalted butter, melted and slightly cooled
¼cup(50 g) granulated sugar
1 ¼cup(150 g) confectioners' sugar, sifted
½teaspoonpure vanilla extract
In a medium bowl, whisk together flour, baking powder and salt. Set aside.
In the bowl of a stand mixer (or using a hand mixer), beat butter and 3/4 cup sugar on high until light and fluffy, about 5 minutes. Beat in egg and vanilla until incorporated. Turn mixer on low and gradually add in flour mixture. Mix until combined.
Divide the dough into two equal parts. Place the dough between two sheets of parchment paper and roll out into a 9"x7" rectangle about 1/4" thick. Remove top piece of parchment paper. Spread one tablespoon of melted butter onto each rectangle. Mix 1/4 cup sugar and cinnamon together then sprinkle evenly over each.
Slowly roll up each rectangle tightly into a 9-inch log, peeling the dough off of the bottom piece of parchment paper. It's okay if the dough cracks slightly, smooth out any cracks with your fingers. Cover the dough log in plastic wrap and chill for 2 hours.
Preheat oven to 350° F. Line a cookie sheet with parchment paper.
Remove dough logs from the refrigerator. Use a sharp knife to cut into 1/2" thick slices. Place slices onto baking sheets about 2 inches apart. Bake for 10-12 minutes, until lightly browned on the sides. Cool on the cookie sheet for 5 minutes, then transfer to a wire rack to cool completely.
Make the Icing
In a medium bowl, whisk together confectioners' sugar, milk and vanilla. Start with two tablespoons milk and if the consistency is too thick to drizzle, add another teaspoon or two. Using a spoon, drizzle icing over the cookies and serve.
Store cookies in an airtight container for up to 5 days.Make ahead instructions: Dough log can be refrigerated for up to two days and frozen for up to 3 months. If you freeze the dough, allow it to defrost in the fridge overnight before slicing and baking.