In a saucepan over low heat, melt the butter, milk chocolate chips and chopped dark chocolate. Remove from heat and leave to cool completely.
In the bowl of a stand mixer or using a hand mixer, whisk eggs and sugar on medium speed for 5 minutes until pale in colour. Add melted chocolate, vanilla extract and espresso and beat until combined.
Add flour, salt, cocoa powder and baking powder and mix until just combined. Fold in chocolate shavings. Cover the cookie batter and chill for 1 hour or overnight.
Pre-heat the oven to 170°C. Line a baking tray with parchment or greaseproof paper. Roll 2 tablespoons into round balls. Place cookies 2 inches apart on baking sheet. Bake for 10 -11 minutes, until the edges are just set and the cookies have crackled. Leave the cookies on baking tray for 5 minutes before moving to wire rack to cool. Eat warm or let cool completely.