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Step 1
In the bowl of a stand mixer beat the butter on high for 1 minutes or until light and creamy. On medium speed beat in the sugar, scraping sides often for 2-3 minutes. Add the egg and vanilla and beat just until combined. Add the flour, baking powder, and salt. Mix on low until combined. If the dough is too soft (unmanageable to touch) add a little more flour 1 tablespoon at a time until it is easier to work with.
Step 2
Divide the dough into 2 equal portions. Roll one portion out on a silicone baking mat sprinkled with a little flour. Roll out to a 10"x8" rectangle or to about 1/4" thickness. Spread with 1 tablespoon of the melted butter.
Step 3
In a small bowl combine the brown sugar and cinnamon for the filling and sprinkle half over the buttered cookie dough.
Step 4
Working very slowly and carefully, tightly roll up the cookie dough into a 10" log. If the dough starts to crack while rolling just use your finger to smooth it out. Wrap the dough in plastic wrap and chill for at least 2 hours but up to 3 days. Repeat with other portion of dough.
Step 5
Preheat oven to 350 degrees F (177 degrees C).
Step 6
Remove dough from the refrigerator and cut into 1/2" slices. Place on baking sheets about 1" apart. Bake for 11-12 minutes or until very lightly browned on edges. Allow to cool on the baking sheet for 5 minutes then transfer to cooling rack to cool completely.
Step 7
In a small bowl combine the ingredients for the icing. Drizzle over completely cooled cookies and allow the icing to dry before storing cookies. Store covered at room temperature for up to 1 week.