Grease a 23cm springform tin with butter and line the base with a round of baking parchment that fits snugly inside. Fill and boil the kettle. Pour 60ml of boiling water over the tea bag and set aside to brew while you get on with the rest.
In a small saucepan, melt the butter for the upside-down figs, then stir in the brown sugar. Cook gently over a low heat for 6-8 minutes until the sugar is melted and the mixture is bubbling. Remove from the heat and pour the caramel into the prepared cake tin. Lay the figs, cut-side up in a concentric circle from the centre of the tin outwards to completely cover the base. Set aside.
Preheat the oven to 180C.
Tip the room temperature butter for the cake batter into a stand mixer with a paddle attachment. Pour in the sugar and beat for 3-4 minutes until pale and fluffy. Beat the eggs in, one by one, waiting until one is completely incorporated before you add the next. The mixture may split, but it will come back together when you fold through the dry ingredients. Add the Greek yoghurt, Earl Grey (discard the tea bag) and orange zest and beat once more just until combined.
In a separate bowl, combine the all of dry ingredients, except the pistachios and whisk to remove any lumps. In three stages, fold the dry ingredients into the wet using a spatula. Continue to fold until no dry patches are visible. Pour the cake batter over the figs in a tin and use the spatula or back of a spoon to even out the top. Slide into the oven and bake for 45 minutes, until a skewer inserted comes out clean. Check after 30 minutes and cover the cake loosely with foil if the surface is turning brown rather than golden.
Allow to cool in the tin for 10 minutes before loosening the springform and carefully inverting onto a cooling rack. Allow to cool completely before scattering with chopped pistachios, slicing and serving with a cup of tea.
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