Melt the butter and honey in a saucepan and simmer until golden brown. Leave to cool. Using an electric mixer, whisk the eggs, caster sugar and brown sugar together for 8-10 minutes, until the mixture has tripled in volume and leaves a trail on the surface for a few seconds when the whisk is lifted.
Fold the sifted flour and melted butter through the egg mixture until it is all incorporated. Pour into a plastic container and leave to rest in the fridge for 2-3 hours.
Grease the Madeleine moulds with butter, and then dust them with flour, tapping off any excess. Place a dessertspoon of the mixture in each mould and bake in an oven preheated to 190C/Gas Mark 5 for 12-15 minutes, until firm to touch and golden brown.