These thin cookies look exactly like tiny frosted cinnamon buns!
Add the egg, scraping down the bowl after it's fully incorporated.
Reduce the speed to low. Add the flour all at once and mix just until combined, about 1 minute.
On a lightly floured surface, roll out the dough to a square about 12 12 inches.
Make the cinnamon smear: In the bowl of a stand mixer fitted with the paddle attachment, mix all the ingredients on medium speed until smooth, about 2 minutes. Scrape down the bowl as needed.
While the dough is firming up, preheat the oven to 375 degrees F. Line two baking sheets with parchment paper.
Using a sharp knife, cut the log into 1/4-inch-thick slices. Transfer the cookies to the prepared baking sheets, spacing them about 1 1/2 inches apart.
Bake until golden around the edges, 12 to 14 minutes. Rotate and switch the baking sheets as necessary for even baking.
Make the icing: Combine all the ingredients in a small bowl. Lightly brush a thin layer on the surface of each cooled cookie. Let set before serving.
Store in an airtight container.