To make the sorbet, combine 200 ml (7 fl oz) of water with the sugar and glucose in a saucepan and bring to a simmer, then allow to cool. Add the honey to the sugar syrup and bring to the boil. Remove from the heat, add the drained, bloomed gelatine to the hot syrup and whisk until incorporated. In a blender, combine the milk and cream, then add the warm syrup to the milk mixture and blend on high for a minute to make sure everything is incorporated. Place in the refrigerator until completely cool. Pour into an ice-cream machine and churn according to the manufacturer’s instructions. Freeze overnight.
Preheat the oven to 190°C (375°F/Gas 5) and grease and line a 20 × 30 cm (8 × 12 inch) cake tin. To make the carrot cake, lightly toast the cardamom pods, cloves, cinnamon stick, coriander seeds, nutmeg and salt, then grind them very finely using a spice grinder. Sift the flour, almond meal, baking powder and ground spices into a large bowl. Whisk the eggs and sugar together in an electric mixer, using the whisk attachment, until tripled in volume and fluffy. Add the grapeseed oil, milk and carrot purée, then quickly incorporate the sifted dry ingredients gently with a rubber spatula, making sure there are no lumps. Pour into the cake tin and bake for 30 minutes. Allow to cool in the tin, then transfer to a wire rack to cool completely.
To make the cardamom caramel cream, put the sugar in a saucepan with a splash of water over medium heat. Cook for 4–6 minutes until it is a medium dark caramel. Slowly add the cream. Let the mixture simmer until the sugar is completely dissolved, then steep the cardamom pods. Cool the mixture down completely, then strain into a clean saucepan and add the carrageenan. Bring to the boil while stirring constantly, then pour into a container and chill. When the gel is firm and cool, purée in a blender until smooth. Set aside until serving.
To make the caramelised honeycomb, combine the honey, sugar and glucose in a saucepan and cook to a light caramel colour. Separately combine 1½ tablespoons of water and bicarbonate of soda in a bowl, stirring to combine. Bring the caramel mixture to 166°C (331°F) using a sugar thermometer, then add the bicarbonate of soda mixture, taking care to whisk constantly so the mixture doesn’t catch and burn. Pour the honeycomb onto a tray lined with baking paper to cool. Break into pieces and set aside.
To make the carrot curd, reduce the carrot juice in a saucepan over medium heat until you have 270 ml (9½ fl oz) with an intense carrot flavour. Whisk the eggs and sugar together in a bowl. Put the reduced carrot juice and agar-agar in a medium saucepan and bring to the boil over medium heat, whisking constantly. Remove from the heat and add the egg mixture, whisking until incorporated. Heat the combined mixture gently until the eggs begin to thicken the mixture, then pour into a blender. Blend on a low setting and start adding the butter slowly so that it emulsifies, but not so slowly that the mixture cools and collapses. When all the butter has been incorporated, pour the mixture onto a tray that you can unmold the curd from when cool.
To make the carrot garnish, warm the sugar, water and vinegar in a saucepan over low heat until dissolved. Marinate the shaved carrots in the dressing until ready to serve.
To finish, swipe some cardamom caramel cream on a plate and add a strip of carrot curd, bookended by hand-torn pieces of carrot cake. Place crumbled and whole pieces of honeycomb on the cake and curd, then add the marinated carrot garnish, edible flowers and finally a quenelle of milk and honey sorbet.