Preheat the oven to 180°C (160°C fan) or 350°F. Grease a 20 cm cake tin and line the base with baking parchment.
Place the chocolate chips in a medium heatproof bowl and melt them gently over a pan of simmering water, or microwave in short bursts until smooth. Set aside to cool slightly.
In a large mixing bowl, whisk together the eggs, vegetable oil, yogurt, honey, and vanilla extract until smooth and fully combined. Fold in the grated courgette. Add the melted chocolate and mix gently until incorporated.
Sift together the plain flour, cocoa powder, bicarbonate of soda, baking powder, and sea salt. Gradually fold these dry ingredients into the wet mixture, being careful not to over mix.
Pour the batter into the prepared cake tin and smooth the surface. Bake for 35–40 minutes, or until a skewer inserted into the center comes out mostly clean with a few moist crumbs. Let the cake cool in the tin for 10 minutes, and then transfer it to a wire rack to cool completely.
While the cake is cooling, make the chocolate icing. Heat the double cream in a small saucepan until just simmering. Pour it over the chopped chocolate and leave for 2–3 minutes, and then stir until smooth and glossy.
Once the cake has completely cooled, pour the chocolate icing over the top and spread evenly with a spatula. Let the icing set slightly before slicing and serving.