Preheat the oven to 160C. Take a 23cm cake tin and lightly oil the tin, removing any excess oil then line the base with baking paper.
Sieve together the baking powder, plain flour and sea salt in a mixing bowl.
Separately, put the caster sugar, marzipan, ground almonds and a tablespoon of the plain flour into a food processor. Grind the mixture until the almond has become finer and the marzipan is broken up further, so that it is all a fine breadcrumb texture.
Add the unsalted butter, vanilla and almond essences and process until fluffy.
Add the blended eggs in stages – firstly add about a quarter and blitz until blended in then add a tablespoon of plain flour and mix, then add the next quarter, blend and add next tablespoon of plain flour and so on. Add the remaining plain flour and pulse a couple of times until it has just mixed together.
Pour the batter into the cake tin, scraping it all in. Put cake mix into the oven and bake for 65 minutes or until the cake is brown on the top and set in the middle.
When you remove it, run a sharp knife around the edge of the cake, then leave to rest and cool completely in the tin. Then remove the cake from the cake tin, take off the baking parchment on the base and dust with icing sugar, should you so wish.