Heat oven to 200C/180C fan/gas 6 and butter a 12-hole madeleine tin or a 24-hole mini madeleine tin. In a small pan, heat the butter over a medium heat until frothy and golden with a nutty aroma. Leave to cool.
Sieve the flour and cocoa into a large bowl, then stir in the egg yolks, honey, coffee, melted butter and both sugars. Whisk the egg whites until stiff peaks form, then fold into the cocoa mix.
Spoon the mixture into the tin, half-filling each of the madeleine holes. Chill in the fridge for 1 hr.
Bake for 7 mins if using a 24-hole mini madeleine tin, or for 10-12 mins if using a 12-hole tin. Remove from the oven and leave to cool.
Melt the white chocolate in the microwave in short bursts, then drizzle over the madeleines.