Preheat oven to 190C. Grease and line a 26 x 19cm slice tin. Prepare an ice bath. Turn ice cream machine on to pre-chill according to manufacturer’s instructions.
For the Sponge Cake, place softened butter in the bowl of an electric mixer fitted with a paddle attachment and beat until pale and fluffy.
Add sugar and continue to beat until mixture is light and creamy.
Add eggs one at a time and beat well after each addition.
Fold through half the flour til just combined. Fold through remaining flour and lime zest and mix until all ingredients are combined.
Pour the batter into the prepared tin and bake about 25 minutes or until golden and cake springs back when lightly pressed in the centre. Remove cake from oven and allow to cool in the tin for 5 minutes, then turn out onto a cake rack and set aside to cool until needed.
For the Smoked Vanilla Ice Cream, heat milk and vanilla and 1/3 of the sugar in a medium saucepan over a medium heat until sugar has dissolved but mixture is not boiling.
Meanwhile, place egg yolks and remaining sugar in the bowl of an electric mixer fitted with a whisk attachment and whisk until pale and fluffy.
Add warmed milk to egg mixture and whisk continuously until mixture is thick and smooth.
Return the anglaise to the saucepan over medium heat and cook, stirring continuously, until mixture has just thickened.
Transfer the anglaise mixture to a medium bowl and place over ice bath to cool.
Once mixture is cool, stir through cream until well combined, then pass through a fine sieve. Cover the mixture tightly with cling film.
Fill a smoking gun with hickory chips and light. Pierce the cling film with the nozzle of the gun and allow the smoke to fill the bowl of anglaise mixture. Once bowl is full of smoke, seal tightly with another layer of cling film and allow the mixture to smoke for 10 minutes.
Once mixture is smoked, pour anglaise into ice cream machine and churn, according to manufacturer’s instructions. Once ice cream is churned, transfer to an airtight container and place in the freezer to firm until needed.
For the Miso Glaze, make a sugar syrup by combining sugar and water in a small saucepan. Bring to the boil and reduce until thickened slightly. Whisk in miso then remove from heat. Set the glaze aside to cool until needed.
To serve, use a 10cm round cutter to cut 4 discs from the cooled cake. Place one cake disc in the middle of each serving plate. Drizzle the top of the cakes with Miso Glaze. Top with quenelle of ice cream.