1. Add the butter and both sugars to a large bowl and mix until very light and fluffy. Add the egg, vanilla extract, and lime juice and mix until well combined. Mix the flour with cornstarch, ground cinnamon, baking powder, baking soda, and salt in a separate bowl. Add to the large bowl and mix until just combined. Place the dough in the fridge for about 1 1/2-2 hours.

2. Preheat the oven to 350°F (180°C). Line a baking sheet with baking parchment and set aside. Mix the brown sugar and ground cinnamon for the coating in a small bowl. Divide the dough into 12 portions, shape them into balls, and roll them in the sugar-cinnamon mixture (there should be some leftovers for decorations later). Flatten the balls slightly and place them with enough space in between on the baking sheet – they spread a bit. Bake the cookies for about 10-11 minutes. Take the cookies out of the oven and let them cool down for some time on the baking sheet, then transfer to a wire rack and let cool down completely.

3. Add the butter and confectioners’ sugar to a large bowl for the churro buttercream, and mix until light and fluffy. Add the cream cheese and mix until well combined. Next, add the brown sugar, ground cinnamon, and vanilla extract and mix until well combined. If the cream is very soft, place it in the fridge for about 30 minutes, then mix again shortly. Fill the buttercream into a piping bag with a star tip, and pipe swirls onto each cookie. Sprinkle with some sugar-cinnamon mixture and serve. Store leftover cookies in the fridge for up to 3 days. Make sure the cookies come back to room temperature before enjoying them.