In a large bowl or stand mixer, cream the butter and sugar until pale and fluffy.
Beat in the egg and vanilla extract.
In a separate bowl, whisk together the flour, cinnamon, and salt. Gradually add to the wet mixture until a dough forms.
Shape into a disc, wrap in cling film, and chill for at least 1 hour.
Preheat the oven to 175°C (350°F) and line two baking trays with parchment paper.
Roll out the chilled dough to about 0.5 cm (1/4 inch) thick. Cut out leaf shapes, use the embosser to emboss the leaf design onto the cookies and place on the prepared trays.
Bake for 8–10 minutes, until just set and lightly golden at the edges. Cool completely on a wire rack.
Make the buttercream.
In a large bowl or stand mixer, beat the butter and brown sugar together until light and fluffy – about 2–3 minutes.
Add the icing sugar and cinnamon, mixing on low speed at first to avoid clouds of sugar.
Add the milk or cream and beat on high until smooth and creamy.
Pipe or spread the buttercream onto half of the cookies, then sandwich with the rest.