These thin cookies look exactly like tiny frosted cinnamon buns!
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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.