In a medium-sized bowl, stir together the flour, baking powder, cinnamon, and salt. Set aside.
In the body of a stand mixer with the paddle attachment, mix the butter until smooth. Add the sugars and mix on medium speed until light and fluffy, about 2-3 minutes. Then add the egg and vanilla extract and mix until well combined. Stir in the dry ingredients slowly in 2-3 additions, stirring until well combined, scraping down the sides of the bowl as needed. The dough should be soft but not sticky.
In a small bowl, combine the sugar and cinnamon and stir until the cinnamon is evenly distributed throughout. Set aside.
Divide the prepared dough into two equal portions (we are making 2 logs here), place one on a floured surface, and roll into a 9x6 rectangle (dough should be about a ¼-½ inch thick).
Spread half the melted butter along the surface of the rolled dough, then sprinkle with half the cinnamon sugar. Carefully roll the dough starting with the longer edge until a log is formed, then wrap with saran wrap and allow to chill in the refrigerator for at least 2 hours. Repeat with the remaining dough to end up with two dough logs.
Remove the chilled dough from the fridge, and preheat the oven to 350°F/180°C.
Slice into ½” inch cookies. Each log will give 15-16 cookies, not including the end pieces.
Place the sliced cookies onto a cookie sheet lined with parchment about 1 inch apart, then bake in a preheated oven for 8-10 minutes, or until puffed and lightly golden. Keep in mind that these cookies do not spread a lot, so you might be able to fit more on a cookie sheet than you usually do.
Allow the cookies to cool completely on a wire rack before drizzling them with the vanilla icing.
In a small bowl, stir together the powdered sugar, vanilla extract, and heavy cream until smooth and desired consistency is reached. Drizzle the cooled cookies with the icing.
Notes
Chill the Dough: It is very important that you chill the cookie dough before you bake. This will help the logs firm up, so you can easily cut them into cookies, and will help with the texture of the cookies so they don't spread out too much and lose their cinnamon roll shape.
Parchment Paper: I found it easiest to roll the dough logs using a piece of parchment to help guide the dough.
Cookie Thickness: Using a sharp knife slice into ½” inch cookies. The cookies can’t be cut too thick otherwise the outer layers may fall over during baking and the cookies won't look good.
Place the unbaked cookies on a cookie sheet about 1 inch apart. Keep in mind that these cookies do not spread a lot, so you might be able to fit more on a cookie sheet than you usually do.
Size: You should get around 30 cookies that are around 1.5" inches in diameter.
Freezing: You can freeze baked cookies, unbaked cookies, and even the cinnamon roll log if you like. Freeze for up to 3 months.