Preheat the Oven: Set your oven to 175 °C (350 °F) to get it nice and ready for your cake.
Chop the Chocolate: In a thermomix or food processor, chop the 80 g of dark chocolate for 6 seconds on speed 8. Make sure to scrape down the sides of the bowl.
Melt the Butter: Add 30 g of butter to the chocolate and heat for 2 minutes at 50 °C on speed 2. Once melted, reserve this mixture and clean the bowl.
Mix Wet Ingredients: In the same bowl, add 30 g of melted butter (for cake), natural yogurt, powdered sugar, and vanilla extract. Mix for 30 seconds on speed 4.
Add Eggs and Dry Ingredients: Add the eggs, flour, and baking powder to the bowl. Mix for another 30 seconds on speed 4.
Divide the Batter: Split the batter into two equal parts. Stir in 50 g of pistachio puree into one part and fold in the melted chocolate mixture into the other part.
Assemble the Cake: Pour alternating spoonfuls of the pistachio and chocolate batters into a buttered and lined 20x8 cm cake pan.
Bake the Cake: Place in the oven and bake for 43-45 minutes. Once done, allow the cake to cool completely.
Frost the Cake: For the frosting, begin by preheating the oven to 160 °C. Spread 30 g of pistachios on a lined baking sheet and roast them for 15 minutes. Let them cool.
Prepare the Frosting: In the bowl, chop the roasted pistachios for 2-3 seconds on speed 6. Next, add 180 g of chopped dark chocolate and chop for 6-8 seconds on speed 8. Melt for 6 minutes at 60 °C on speed 2, then add 40 g of neutral oil and mix for 20 seconds on speed 3.
Finish the Cake: Let the frosting cool slightly and pour it over the cooled cake. Garnish with chopped pistachios and refrigerate until the frosting sets.