Grease and line the base of a 22 cm(8½ inch) springform tin. Put the butter, brown sugar and honey in a small saucepan and add 1 tablespoon of water. Heat gently, stirring once or twice, until the butter melts and the sugar dissolves. Leave to cool for 15 minutes. Preheat the oven to 180°C (350°F/Gas 4).
Sift the flour, baking powder and cinnamon into a bowl and add the rosemary. Add the honey mixture and eggs and beat until smooth.
Pour into the tin and bake for 35–40 minutes, or until a skewer comes out clean when you poke it into the centre. Leave in the tin to cool completely.
To make the lemon icing, sift the icing sugar into a bowl. Add the butter, lemon zest and juice and 1 tablespoon of water and beat until smooth. You might like to add a few more drops of lemon juice after tasting it. Spread over the top and side of the cake. The cake softens as it sits and will keep well for up to a week in a cake tin.